Although the request was for Yakketty, it also has the the bug in Xenial. I did try to manually download arial32.exe and andale32.exe using wget and then copying them to /var/lib/update-notifier/package-data-downloads/partial. Doing so allowed the reconfigure to succeed.

sudo apt show apt-transport-https
[sudo] password for admin0: 
Package: apt-transport-https
Version: 1.2.19
Priority: standard
Section: admin
Source: apt
Origin: Ubuntu
Maintainer: Ubuntu Developers <email address hidden>
Original-Maintainer: APT Development Team <email address hidden>
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Installed-Size: 213 kB
Depends: libapt-pkg5.0 (>= 1.1~exp15), libc6 (>= 2.14), libcurl3-gnutls (>= 7.16.2), libgcc1 (>= 1:3.0), libstdc++6 (>= 5.2)
Recommends: ca-certificates
Task: standard
Supported: 5y
Download-Size: 26.0 kB
APT-Manual-Installed: yes
APT-Sources: http://us.archive.ubuntu.com/ubuntu xenial-updates/main amd64 Packages
Description: https download transport for APT
 This package enables the usage of 'deb https://foo distro main' lines
 in the /etc/apt/sources.list so that all package managers using the
 libapt-pkg library can access metadata and packages available in sources
 accessible over https (Hypertext Transfer Protocol Secure).
 .
 This transport supports server as well as client authentication
 with certificates.

[Before file downloads]
sudo apt-get install --reinstall ttf-mscorefonts-installer
[sudo] password for admin0: 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following packages were automatically installed and are no longer required:
  linux-headers-4.4.0-64 linux-headers-4.4.0-64-generic
  linux-image-4.4.0-64-generic linux-image-extra-4.4.0-64-generic
Use 'sudo apt autoremove' to remove them.
0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 2 not upgraded.
Need to get 29.5 kB of archives.
After this operation, 0 B of additional disk space will be used.
Get:1 http://us.archive.ubuntu.com/ubuntu xenial/multiverse amd64 ttf-mscorefonts-installer all 3.4+nmu1ubuntu2 [29.5 kB]
Fetched 29.5 kB in 0s (84.9 kB/s)                  
Preconfiguring packages ...
(Reading database ... 421788 files and directories currently installed.)
Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ...
mscorefonts-eula license has already been accepted
Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) over (3.4+nmu1ubuntu2) ...
Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ...
Processing triggers for update-notifier-common (3.168.3) ...
ttf-mscorefonts-installer: processing...
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe
Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB]
Fetched 198 kB in 7s (27.2 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe
Err:1 http://downloads.sourceforge.net/corefonts/arial32.exe
  Protocol "http" not supported or disabled in libcurl
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
E: Failed to fetch https://dronedata.dl.sourceforge.net/project/corefonts/the fonts/final/arial32.exe  Protocol "http" not supported or disabled in libcurl

E: Download Failed
Setting up ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ...

[After downloading arial32.exe and andale32.exe]
sudo apt-get install --reinstall ttf-mscorefonts-installer
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following packages were automatically installed and are no longer required:
  linux-headers-4.4.0-64 linux-headers-4.4.0-64-generic
  linux-image-4.4.0-64-generic linux-image-extra-4.4.0-64-generic
Use 'sudo apt autoremove' to remove them.
0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 2 not upgraded.
Need to get 0 B/29.5 kB of archives.
After this operation, 0 B of additional disk space will be used.
Preconfiguring packages ...
(Reading database ... 421788 files and directories currently installed.)
Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ...
mscorefonts-eula license has already been accepted
Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) over (3.4+nmu1ubuntu2) ...
Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ...
Processing triggers for update-notifier-common (3.168.3) ...
ttf-mscorefonts-installer: processing...
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe
Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB]
Fetched 198 kB in 2s (78.4 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe
Get:1 http://downloads.sourceforge.net/corefonts/arial32.exe [554 kB]
Fetched 554 kB in 6s (91.8 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arialb32.exe
Get:1 http://downloads.sourceforge.net/corefonts/arialb32.exe [168 kB]
Fetched 168 kB in 3s (45.3 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arialb32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/comic32.exe
Get:1 http://downloads.sourceforge.net/corefonts/comic32.exe [246 kB]
Fetched 246 kB in 1s (179 kB/s)                                                
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/comic32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/courie32.exe
Get:1 http://downloads.sourceforge.net/corefonts/courie32.exe [646 kB]
Fetched 646 kB in 4s (132 kB/s)                                                
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/courie32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/georgi32.exe
Get:1 http://downloads.sourceforge.net/corefonts/georgi32.exe [392 kB]
Fetched 392 kB in 22s (17.7 kB/s)                                              
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/georgi32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/impact32.exe
Get:1 http://downloads.sourceforge.net/corefonts/impact32.exe [173 kB]
Fetched 173 kB in 6s (25.4 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/impact32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/times32.exe
Get:1 http://downloads.sourceforge.net/corefonts/times32.exe [662 kB]
Fetched 662 kB in 9s (68.1 kB/s)                                               
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/times32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/trebuc32.exe
Get:1 http://downloads.sourceforge.net/corefonts/trebuc32.exe [357 kB]
Fetched 357 kB in 1s (231 kB/s)                                                
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/trebuc32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/verdan32.exe
Get:1 http://downloads.sourceforge.net/corefonts/verdan32.exe [352 kB]
Fetched 352 kB in 1s (231 kB/s)                                                
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/verdan32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)
ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/webdin32.exe
Get:1 http://downloads.sourceforge.net/corefonts/webdin32.exe [185 kB]
Fetched 185 kB in 1s (137 kB/s)                                                
W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/webdin32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)

These fonts were provided by Microsoft "in the interest of cross-
platform compatibility".  This is no longer the case, but they are
still available from third parties.

You are free to download these fonts and use them for your own use,
but you may not redistribute them in modified form, including changes
to the file name or packaging format.

Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/andale32.exe
  extracting fontinst.inf
  extracting andale.inf
  extracting fontinst.exe
  extracting AndaleMo.TTF
  extracting ADVPACK.DLL
  extracting W95INF32.DLL
  extracting W95INF16.DLL

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/arial32.exe
  extracting FONTINST.EXE
  extracting fontinst.inf
  extracting Ariali.TTF
  extracting Arialbd.TTF
  extracting Arialbi.TTF
  extracting Arial.TTF

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/arialb32.exe
  extracting fontinst.exe
  extracting fontinst.inf
  extracting AriBlk.TTF

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/comic32.exe
  extracting fontinst.inf
  extracting Comicbd.TTF
  extracting Comic.TTF
  extracting fontinst.exe

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/courie32.exe
  extracting cour.ttf
  extracting courbd.ttf
  extracting courbi.ttf
  extracting fontinst.inf
  extracting couri.ttf
  extracting fontinst.exe

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/georgi32.exe
  extracting fontinst.inf
  extracting Georgiaz.TTF
  extracting Georgiab.TTF
  extracting Georgiai.TTF
  extracting Georgia.TTF
  extracting fontinst.exe

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/impact32.exe
  extracting fontinst.exe
  extracting Impact.TTF
  extracting fontinst.inf

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/times32.exe
  extracting fontinst.inf
  extracting Times.TTF
  extracting Timesbd.TTF
  extracting Timesbi.TTF
  extracting Timesi.TTF
  extracting FONTINST.EXE

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/trebuc32.exe
  extracting FONTINST.EXE
  extracting trebuc.ttf
  extracting Trebucbd.ttf
  extracting trebucbi.ttf
  extracting trebucit.ttf
  extracting fontinst.inf

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/verdan32.exe
  extracting fontinst.exe
  extracting fontinst.inf
  extracting Verdanab.TTF
  extracting Verdanai.TTF
  extracting Verdanaz.TTF
  extracting Verdana.TTF

All done, no errors.
Extracting cabinet: /var/lib/update-notifier/package-data-downloads/partial/webdin32.exe
  extracting fontinst.exe
  extracting Webdings.TTF
  extracting fontinst.inf
  extracting Licen.TXT

All done, no errors.
All fonts downloaded and installed.
Setting up ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ...