Toyota Corolla DX Wagon 1995 transmission problem

I wrote here a while back but having lived with this problem a while I can give more details and maybe this will get me a better answer.. the car is a 1995 corolls DX wagon. Automatic transmission. about 135000 miles.
   
The transmission seems to have a serious issue.. When I start driving it, the speedometer bounces up and down, and the car cant tell what gear it's supposed to be in. so it revs up real high and doesn't go any faster. after between 5 and 15 minutes of driving the problem goes away and the car acts and shifts normal.. even for long road trips. Although occasionally the speedometer will drop to zero on the interstate and cruise control will stop working. That's not a huge issue because once its going that fast shifting is not an issue.

I have lived with this problem for close to 2 years and I believe it was an issue before I got the car (for free). In all that time the problem has not gotten worse, although I am paranoid it will just go out completely one of these days. My local mechanic (who doesnt specialize in transmissions) couldnt figure it out. We tried replacing the speed sensor. That didnt fix it.

I suppose with a car this old I might be better off just getting a new car. But it is sentimental to me and since I got it for free I am willing to spend a little bit of money on it... especially considering its in good shape and has been well maintained other than this issue.