You know, working on airplanes really doesn't have much in the way of transferable skills to drywall repair.
Except the important bits: learning how to prep for a project, and clean up as you go along. Gracious, but drywall is messy!
Anyway, I still had the best two fallbacks: youtube videos, and calling my Dad for a sanity check. There was also a quick discussion with OldNFO & LawDog, who agreed with Dad - instead of screwing a backer board behind the repair, the wiser thing to do was to enlarge the hole until I found a stud, and screw the drywall patch into the stud. I still find it a little strange that the repair process starts with "Make a much bigger hole", but it makes sense!
Patches are now cut out, put in, taped, mudded, and awaiting on the mud to cure. It's rather rough, but I am reminded that I"m starting at the very bottom of the drywall repair learning curve, after many years without doing any at all. My first welds, rivets, and brazing were really ugly, too. (In fact, they were less functional than this drywall patch. Drywall definitely has an easier learning curve than riveting.)
And there's still sanding and a coat of paint to clean it all up and make it pretty. If it still looks rough but functional, then when I get better at it, I can do it again!