I had a rare transmission failure in my 96’, with mine, reverse was first to go, at first it would engage after a few seconds and later a I could shift through other gears or in and out of low range to get it to engage after a minute or more, but there was never a situation like you are describing (other than the hotter than normal console). I found very little information on Mud to compare because a transmission failure wit the A442 is so rare, I did eventually find or they found me, an 80 that had a similar symptom as mine.
I am not saying it isn’t the transmission, just mine and the single case I read had similar failure signs, very slow to engage at first until it doesn’t at all.
Several reputable members are pointing to other diagnostics that you should investigate prior to a transmission rebuild/replacement. I agree finding a Cruiser focused shop would be a big benefit, even if it required towing/hauling somewhere else, there isn’t much to be gained by driving it any farther.
Good luck!
Also, If it does turn out to be transmission, I couldn’t find anyone to rebuild mine and ended up installing a used one, actually 2, that is an another story, but because the transmission is historically good, you should be able to find a used one easily.