You must settle the bill for parts and labor before you can take the vehicle, that may or may not be greater than the deposit.
The shop may not be comfortable with you taking the car in a disassembled state, it will cost you about $5,000 for the transmission core and the associated parts that were left behind.
You might have been able to sell the car last month as a car with a transmission problem but as a “parts car” you may only get $2000 to $3000.
The wealthy don’t fit well into a Corolla.