Mystery shifting problem in '89 Maxima

Mom’s taken excellent care of her Nissan since she bought it new. It has a V6 and auto, 140K miles on it and began having starting/shifting trouble last year (i.e., the old mess-with-the-shifter-so-it-will-crank thing, and some serious slippage). My trusted mechanic serviced the transmission and when he dropped the pan found lots of clutch debris, so he recommended replacing it, which we did.
The starting problem was cured, but occasionally she’ll back out of the driveway, put it in Drive, and it will immediately stall, and require several tries (or a few hours’ wait) before it will work again, although reverse always works. This is so intermittent that no one has been able to duplicate it at the shop. Other times, it will start out in second gear and stay there, requiring her to pull over, shut off the ignition, and restart, at which point it drives just fine. Again, the mechanics can’t get it to do this for them.
The electronic shift control module checks out okay, and we are at the point where it would be too expensive to pay smeone to dig into the wiring. All I can think of is some kind of demented ignition/neutral safety switch thing.
Just thought someone might have seen something like this before. Any ideas would be helpful.