Situation Update: It worked!
OK! They released a new build of 10.13 earlier this week so I waited a few days and gave it a try today.
The installation went flawlessly and so far everything looks great.
Oddly, after the installation, I ended up with about 15 GB more free space on my HD and the systems seems quicker ... Even on the first and second boots, and that's unusual based on past experience.
Previous comment from October 3:
This was exactly my problem. Fortunately I completed a Time Machine backup just before the attempt to install High Sierra. After 8 hours (including several on the phone with Apple, I gave up and restored from the Time Machine. Amazingly that went flawlessly and the system is whole again.
One Odd note, when the restore was done, I ended up with about 80 GB more than I had when I attempted the High Sierra Installation.
However, I too have a Late 2012 iMac27 so I think this might be a coincidence and will hold off on another attempt for a while.
Sierra: 10.12.6 (16G29)
iMac (27-inch, Late 2012)
2.9 GHz Intel Core i5
32 GB 1600 MHz DDR3