Well, back from the garage, and now cleaned up enough to test-drive (after I re-reset the adaptations - don't want to risk driving in limp mode screwing up any of the parameters).
I turned the lockring on the connector, and almost immediately got a steady drip-drip-drip of fluid. I didn't really have to go any further than that to know that I really DID have to fix the position of the sleeve. Happily, this also means that I didn't have to fight, wriggle, and bruise myself getting that connector lined up again.
Drained the fluid (into a carefully washed pan) and used a 1x2 about 18" long to wedge between the plug and the transfer case (or mount). That gave me enough umph to sink the sleeve to what is apparently 2.5 to 3mm. I'd inscribed a silver line on the previously protruding portion of the sleeve, and it's clearly quite a bit further into the case now.
TAKEAWAY FOR DIY'ers LOOKING FOR ADVICE: Do what scottalexander suggests, and use something (preferably something sort of soft, like wood) to press the Mechatronics sleeve into the tranny case, or you'll never get it in far enough.
Did a quick check with my handheld scanner, and lo and behold, the tranny is back! Reset all the (MANY!) error codes, and everything looks good.
Put the pan back on (torqueing it to spec again) and filled the tranny with the fluid that I just took out. FWIW, it looked pretty good for having had just one drain-and-fill process. Not pristine, but not the dark, evil looking stuff that came out when I drained it initially.
Now I just have to go drive around in circles and train the tranny to shift again. I'm confident this time it'll go a bit better.
Thanks, scottalexander, for your invaluable help. I owe you a couple adult beverages if you ever make it to Mesa, AZ (soon to be too warm for the COVID-19 virus to survive!).