Hmmm... I have to admit, that's quite a bit different than a standard
Autocontrol (aka Century) for a normal Piper system - and I would ask
if you are sure of your information? The standard "wing level"
indication from the AH is indeed off a pickup coil, but it's about 5
KHz, no RF. And there is no frequency shift - the inside of the
Century AH/AI just has two coils and a metal plate behind them (looks
like an iron butterfly). As the thing shifts from one side to the
other you get a shift in amplitude, either in phase or out of phase
(180 degrees) with respect to the ROLL EXCITATION signal. [Or the HDG
EXCITATION signal, if it goes through the nav coupler.] With the AH
centered in roll, the amplitutde is zero. There is no frequency shift
regardless. It would be great if there was some sensor back from the
ailerons, but there isn't - so it has no way of knowing their position.

Having said all the above, your "list of the usual suspects" is the
same one I would come up with. #3 is the one that surprises most
folks, but if you have a nav coupler then it uses HDG EXCITATION to
drive the ROLL coils, so lose of HDG signal affects just operating in
the WINGS LEVEL mode. You can move the ROLL cable that goes from the
computer to the NAV Coupler to go to the AI instead and restore use of
ROLL EXCITATION for a test.