Report - in case it's helpful to others.
I went through this process, most likely without fixing the problem. Item 6 in the instructions for repairing a Fusion drive says:
"If your Fusion Drive can be fixed with Disk Utility, you'll see a Disk icon with red lettering. Click the disk icon."
I never saw that Disk Icon, and no red lettering, so I suppose my fusion drive could not be repaired.
I let the process run. I tried to make a choice about using the Internal Hard Drive (instead of Flash) for installing the operating system, but that clearly did not work. I think I'm back where I was, only with a lot of things to relocate and re-install. Still, I am glad I gave it a try, so now I can at least assume I know how I have to use the system I have -- manual moves.
I'm novice enough to be surprised that the OSX version the Disk Utility installs is Mountain Lion, when I had been running Yosemite, so there was that update to complete. The good news is that data seems in place. The bad news, of course, is just the effort of reinstalling, reconnecting to online services and so on.
I appreciate your help, Linc Davis.