I am on the pre-buy list for an IFD540.  Started talking to a local avionic shop about the panel work that's going to go along with it, and he said, "Hold up...I'm not sure the IFD540 is STC'd for your autopilot."

I have a Piper Cherokee with a Piper Autocontrol III autopilot.  My GNS430W is currently coupled to it.

Now that installation manuals are available, I can see that there's no explicit listing in Table 55 or section 6.13 for the Piper Autocontrol in the list of compatible autopilots.  However, the Autocontrol III is essentially just a re-badged Century II, which *is* STC'd.

Am I outta luck here, or is there a path through the paperwork for me?

There is a meaningful distinction between proven compatibility and being "STC'd for your autopilot".  There isn't any notion that I'm aware of that couples a given navigator with a given autopilot, at least not in the IFD540 class of navigators.  Our Installation Manual just provides a list of devices that we proved compatibility with ourselves.   I'm not familiar with the Piper Autocontrol III but if the expected input/output matches that of the Century II, then you are good to go.

The IFD540 STC does not limit installation to only a selected set of autopilots.  And, typically, autopilot STCs do not mandate a specific navigator.

If you had a 430W driving the autopilot, then an IFD540 will do just fine too.