Hey. I have two MAS sticks that are roughly 5 years old (PSX). When the dual shock controllers and subsequent games came out, my sticks started bunking. Apparently the encoder chip they used at the time could not handle the 'rumble' signal coming from the psx.
I mention this because my options were send it back to them or do something about it myself. I chose the later, hacking apart a budget psx controller and soldering it in. It was easy and works great. However, I didn't have to worry about leaving their pcb in the stick, which from the sound of it you'd like to keep it in there.
At the time the MAS people were totally open to me sending the stick back and getting the PCB replaced, at a somewhat slimey $25 per stick.
They are pricey but I bet they would be open to having you ship the stick to them, pay for the added controller, and ship it back.
As far as finding and putting on your own chip, I don't see that happening. They are fairly proprietary, and at the very least ambiguous enough to be a lot more work that working in another controller in there.
Hope that helps.