It could be a couple of things. There is an adjustable thermostat that cycles the pump, and that needs re-adjusted for 134a. It's behind the glove box.
You could also have a worn-out expansion valve. They're supposed to balance A/C flow, and they're charged with some R12, but that's probably leaked out by now. New ones will be charged with the 134a and work better anyway.
Lastly, the American Air condenser is bigger, but takes a different receiver/dryer. A bigger condenser will help, and if your old condenser is rotting away, it's not going to do its job very well. The receiver/dryer should have been changed when the 134a was put in. They are usually rusted to the condenser.
The only part that is really refrigerant specific is usually the expansion valve, but because 134a is just a little less efficient a bigger condenser can help, especially in cars where the original condenser may have been just sufficient. The evaporator in our cars is plenty big if it's getting enough cool refrigerant.