Invest the money into something that can be worth something?? Like a 401k/ROTH or similar, it's honestly a smarter choice than dumping it into a car almost not worth the $2500 max you have to spend.
If you can't achieve your goal of 13's for under $1,000, just sell the car. It wouldn't be worth it to go further and at this point you have a $2-3k transmission calling your name at any minute, and then it's really not worth it. One wrong downshift and it'll blow this budget out of the water.
I know this is a harsh and semi mean post, but it's the reality.