I just wanted to say that I appreciate everyone's help!
I wasn't able to get "Wish I Were..." configured to mimic a SCSI bus and map my IDE drive to disk IDs. Setting it up as an older Performa didn't allow "Apple Restore," which I found on the "Utilities Disk" of an old 7.01 floppy. But the suggestion to try "Wish I Were..." prompted me to look into SoftMac, which ran the 7.01P "Apple Restore" program on my floppies just fine.
Only out of curiosity, I'll check back to see if anyone knows how to make "Wish I Were..." (or using MacsBug for that matter) create a Gestalt set that looks like a SCSI bus.
I'll note that Apple doesn't seem to have "Apple Restore" in its FTP downloads areas that I could find. That could pose a potential problem for others who run into my situation with old backup sets.
Thanks again to all. I've enjoyed the nostalgia more than I expected. What a wonderful system MacOS truly has been. Also, Apple Support was very kind in referring me to this site for questions, after doing their best to help out over the phone.