I am not aware that there is any multiple STCs for installing the Century A/P in an AA-1X. This might have been done under a 1 time STC, but you would need to track down someone that has done it. If so, it was likely done 30 or 40 (even 50) years ago, when you might find a local FISDO office that would work with you an such an installation. Times have changed and with it the FAA mindset.
The only A/P that has been STCed in the AA-1 series that I am aware of is the Brittain A/P in the AA-1 Yankee only, this was never extended to the rest of the AA-1 series (SA2104WE issued in 1970).
So it will be hard to find any documentation on installing a Century in an AA-1A.

While looking for something else I stumbled across this STC – SA1472SW
“Installation of Mitchell Automatic Flight System Model AK373 consisting of Century I Autopilot with optional Omni Tracker”.
Again, only for the original AA-1 Yankee (not AA-1A or later).This was issued to Century Flight Systems Inc. Checking their website it does show this under approved STCs.

I have the C1 w Nav steering installed on my AA1 and have the operation manual but not the installation manual. Works great!