I think I'd try to narrow down the problem with help from the guys on here. A shop is going to have trouble narrowing down a random problem like this.

Here are the options I see:

1) If you can't resolve the starting/running issues, get rid of it.

2) If you figure out the engine problem, put a shift kit and trans cooler in for less than $100 and see how long you can go.

3) If the engine, shift kit and cooler, buy you some time you may eventually need a different transmission. At that point in time, review your options. If you decide to replace the transmission, get a used one instead of a rebuild. To buy and have it installed should cost less than half of the $1500 you stated.

If you end up selling, you'll have to decide if parting out is worth your time or if you just want the car gone.