Unable to install

Try running the memory check which is a menu choice on the install media.
Try running the media check too, a dirty drive may be causing problems.
Seatools checks the hard disk, but not the filesystem, so if you can boot a live media into "try" mode, run the file system check on the hard disk partition (try just fsck /dev/sd??? with the installation you installed to).

it freezes at some point in the process
=> which one ?
I got error messages regarding missing grub files
=> which error messages ?
=> https://help.ubuntu.com/community/Grub2#Reinstalling_GRUB2

Unfortunately I didn't write down the nature of the missing files that precipitated my trying to reload, the computer just said that there were missing grub files.

Currently, the installation process halts at "Creating ext4 file system for / in partition #1 of SCS14 (0,0,0) (sda)... 33%"

It gets no farther than that. I set everything the simplest way I could, it's erasing the existing partitions to use the whole disc, not downloading anything extra or updating as it installs

A failure during creation of file system doesn't look good.
When the message was displayed, did you continue to hear disk activity ? Perhaps it's the display which froze.
Else it could means your hard disk has hardware issue. Is the disk new ? Does it makes click ? Could you boot on Ubuntu CD, choose "Try without install" and then System->Administration->Disk Utilities: SMART Data.

My initial feeling is that this is a HD issue. Sadly, this happens every 8 months or so, this occurrence is unique in that the HD isn't messed up in some obvious way.

A few moments after the stopping point described above, the HD does go silent. The fans continue to run and the display that expounds the virtues of Kubuntu continues it's slide show, but there is no apparent HD activity. The disk is not really new or old, I think I got it early last March or April. According to SeaTools, SMART has not been tripped. I just ran a memory check from the .iso disk and it's clean.

I'll check the SMART data through the iso, but I think I just need a new HD. I'm done with SeaGate, I've bought 5 of their drives in the last three years and they all have gone bad in less than a year.

I really appreciate the time you put into trying to answer this question, it is frustrating not having my machine working, but knowing I have great free tech support like this place makes it all much easier to deal with.

Has anyone had any experience running Ubuntu off a small SSD drive with a larger HD for data?

Some people have, but not me.
I saw some issues on SSD, but as I'm answering in a forum to fix problem, I see only bad news, never good ones! At installation, I think it could be safer to make a dedicated 1GB partition dedicated to /boot folder on HDD. It seems that sometime the SSD drive is too fast for software! I can't tell you which percentage of SSD installations have issue.

Did you ever check your memory?
You could boot from the install media and make the filesytem directly with mke2fs. Use the -c option to check for bad blocks. See the manual pages (man badblocks and man mke2fs).
I've had pretty good luck using 4G usb sticks as root filesystems. Some initial setup of the stick to improve performance like setting the h=4 and s=16 for the disk geometry in fdisk and starting partitions on 4M boundaries (typically only the one partition is needed, no swap). Just install to the stick and put grub on it. then you can edit the /etc/fstab and put things like /tmp and /var/log on it. I also set up a user whose home is in ram (on /tmp), and unpack the home from a command in rc.local. Also for flash homed user, link the browser cache to a /tmp directory.
@delance -- I've a writeup of how I set these usb sticks up, and noticed you had done some "howtos" -- is there a place to upload the writeup? It's just a text file at this point.

@Ubfan:
Someone a day declared a project Grub. In fact, it was an empty shell. But it allowed me to create FAQs on Grub. The Ubuntu's way should be to make a FAQ linked to project Ubuntu instead, but there are so many item that I was not able to use it.
Theoretically, Launchpad, when a new question is asked, should be able to scan whole Ubuntu's project FAQ, to see if some match.
Practically, I use Grub FAQ to store pre-defined answers and requests to user. I found it's a good way to upload writeup. I never had the courage (and time) to make a help.ubuntu doc. It should be good if this FAQ will be increased with more entries about Grub and also more general installation entries.
The packet hierarchy is too small, and forum lacks some more wide category like Installation process, Network, Graphic, Sound and so on.

@delance: Thanks, I'll look around some more. I have a friend putting it up (eventually) on a user group site, and just wanted to be able to link to something public. I'm going through the txt to html exercise and found markdown does the job for me.

Original issue was apparently the hard drive. Replaced it today with a Western Digital and reloaded without incident.

Thanks for taking the time to help me out.