Too many restarts ... I am back to Sierra! But it wasn't easy. Here is the rest of the story ...
Let me first say that the Beta is still running fine on my MacBook Pro with no problems. I also have iOS11 Beta running on my iPhone 6+ and iPad Pro with absolutely no problems. Note that I did have to delete all 32 bit apps on the iOS devices, since they are no longer will even launch. (If you are running iOS10 you can see which are the 32 bit apps by going to Settings > General > About > Applications to get a list.)
Before upgrading to 10.13 on my iMac, I did, of course, make a bootable backup using Super Duper. The backup and upgrade did go smoothly, but after a few days I was having a lot of "spinning beachballs" and restarts, so I decided to downgrade back to 10.12. That is when I discovered that the current version of Super Duper will not function under 10.13 (something about SIP restrictions), so restoring using Super Duper was not an option.
So then, I decided to boot from my backup copy and just download the 10.12 installer and use it to restore my internal hard disk. That concept also failed, since the installer will not work on a system that is "newer" (the 10.13 beta).
Then, I decided to use the Restore feature of Disk Utility to copy the entire contents of my backup disk to the internal disk, which worked but took quite a while. Once completed, however, I discovered that for some reason I could not boot from the internal disk ... it just hung about 10 seconds into the boot process.
Finally, to get back to having a bootable 10.12 internal drive, I had to boot from the backup and do a fresh 10.12 install on the internal drive. All in all, quite a long process ... but at least my iMac is working normally again.