To update my portion of this thread, JIC anyone is curious what happened (granting that my experience is anecdotal; YMMV):
Took some time after i engaged this thread, and needed the car to more consistently behave poorly, until i took my little list of known issues with the 1st gen 8-AT, my wife's mother's deceased husband's death certificate, and clearly and calmly stated the case.
For clarity – the car was not serviced at the same dealership prior to my wife getting the car, and hadn't been downstate where it was originally purchased since the 2016 death of my wife's mother's husband (she remarried well after my wife was grown), so the familial connective tissue was pretty thin.
At any rate, it took a bit of back and forth, some of which was between the not-quite-local Hyundai dealership (went to another, just across state lines b/c the local has pretty shoddy reviews and reputation – interestingly corroborated by the chosen dealer when i explained why we went there vs the closer dealer; "yeah, we've heard that about them...") and Hyundai corporate, but after a couple/few days, we were informed (i had to call and ask) that Hyundai would address the transmission problem, but wouldn't cover ancillary and unrelated...blahblahblah.
Worked in our favor (?) that by the time i got the '12 to them, it was pretty swiftly and consistently exhibiting the between-gear change disengage feeling and RPM surging. They confirmed the problem straightaway, determined that a required procedure/testing did not correct the problems, and let us know a couple of days later that Hyundai corporate authorized replacement of the transmission with a reman (i had to ask).
That was ahead of expiration of both 100k and 10-yr warranty coverage (approx 6500mi and 8 mo) and was completed in just over a week, back in January of this year.
I also had to ask for a rental/loaner, which they granted without push back, and the week + (Hyundai insists on the rental being a Hyundai, so we ended up with a '21 Elantra for the duration) may have gone on longer had i not been the squeaky
wheel in pestering for information.
Since we got the car back, it's been operating fine/normally, and of course we're exceedingly pleased that the transmission problem was resolved.
If i were to find something of which to be critical, it would be that i had to persist at every step of the process.
The dealership was not forthcoming with any communications, wouldn't have covered an Enterprise rental had i not asked, and it seems would not have let us know the car was done had i not finally called over a week after the car was deemed qualified for the reman trans.
Found i was doing a bit of a dance between giving enough space so as not to be the person who calls for constant updates, but also not falling off the radar – but really minor inconveniences to pay.
Again, that's finding something to be critical of, because as far as addressing and resolving the REAL issue, Hyundai did so, in this particular situation.
Appreciate the input from forum veterans, as running it past y'all here provided me both an avenue for your considered insights, and enough additional confidence to approach Hyundai with our problem.
I needed to get out of my own head, and away from the caterwauling
ladies from whom i wrested the situation.