Recovering FDE Ubuntu/Grub after (re-)installing Windows

Hi,

How do I repair/recover my Grub after reinstalling Windows 7 if my Ubuntu (16.04) had full-disk encryption enabled?

I'm an Ubuntu user but kept Windows around as a dual-boot. I had it set up as people normally do, with the Grub screen coming up and Ubuntu booting by default, but with Windows as an option. I recently went into Windows to test out relative performance of a game. I was updating the AMD graphics driver in Windows when the machine crashed, leaving the driver half-installed. The Windows machine then failed to boot. To fix that, I reinstalled Windows.

Unfortunately, reinstalling Windows overwrote Grub and it just booted into Windows without the ability to boot into Ubuntu. I tried following:
https://help.ubuntu.com/community/RecoveringUbuntuAfterInstallingWindows
There were no special instructions for FDE installs, so I just set up a boot-repair boot disk and did the "Recommended Repair". That didn't do anything. I went back in and decrypted the FDE disk first, then ran the tool. No joy. I then tried to make some sensible guesses on the advanced options. Still no luck.

I can obviously reinstall Ubuntu on the machine to fix this, but I hope there is a better way. If there is, I would also like to update that help page to help others stuck in this situation, so I thought I'd ask.