first i would check (or replace) the shift solenoid for 1st to 2nd
i dont think your tranny is going bad--it definately sounds electrical....
i had a similiar (if not the same) problem on my 96 AW-4, and it turned out to be a bad tranny computer
the computer on my 96 is a small black box, about the size of a deck of cards, located under the dash on the passenger side.
i ended up buying a brandnew one at the dealer....i think it was like $180 IIRC
that solved all my tranny problems, just like u described
now, for my 96 at the dealer, they had 2 choices of computers, the regular one and the police pkg one....i asked the parts guy what the difference was between them, and (of course) he didnt know
i would guess it may make shift points higher and harder, but im just guessing
the parts guy said if i dont already have a police pkg jeep, then i shouldnt get the police tranny computer because it may not be compatible with my rig.......i dont know if i believe that, but i ended up getting the regular one anyway
hope this helps
CaptTrev