Finally, after some research and tinkering, I was able to update Hackintosh High Sierra successfully. Then I tried installing Developer Beta 8, and had similar symptoms. I discovered it on my own Hackintosh when I tried first to update to High Sierra Public Beta 7. Apple seems to have upped the ante a bit for Hackintosh users who want to run the latest beta build.
There’s another obstacle to installing or upgrading the latest version of macOS High Sierra on a Hackintosh, but I’ve got an answer that worked for me.