You might need a new radiator. The stock tranny cooler is inside it and if it's leaking into the coolant then most likely even bypassing it you're going to have to deal with coolant leaking into the now empty transmission cooler. You might want to rent a radiator pressure tester from vatozone and check out the condition of the radiator.

A new radiator is not that expensive aftermarket and add 100 bucks for having the transmission flushed.