I tried three methods. I've owned Macs since my first Classic in the 80s so I do understand them fairly well.
I had a bootable High Sierra that I had used previously to install on two desktop pros and one iMac. That was my first attempt and I tried it several times with the same negative result.
I tried Command R. Disc Utility could not unmount so I couldn't do first aid. In Recovery it would open an installer and go through the entire process to the bitter end and then say the same thing - that Mac OS could not be installed on this computer.
I did have a time machine backup. I could not get to it because the system did not show files and would not open a finder search window.
I tried using CCC that was on a usb enclosure with a 1TB HDD. CCC could not see the iMac.
There was no way I could see any of the files on the iMac. Just a blank page even though it did boot. I also tried starting in safe mode but still no files showed up. I used pram reset to no avail. However it would always go into recovery mode but would not finish the installation, stopping at the very end with the same message.
So I gave up. In recovery disc utility I erased the drive.
I made a new bootable installer and with the erased drive I was able to install High Sierra. I had lost some very important files that are not on Cloud. The resulting installation looked nothing like what I had before though and now there is yet another problem:
The sound preference has only sound input options of microphone or line input. So I have no sound from videos or iTunes. And it refuses to install Soundflower which always has worked before.
At least I can use the iMac again even though I lost everything.
Thanks for your time.