So, trying to save some cash, I purchased the AF-360FGZ foot directly from Pentax and upon receiving it, I found that it was actually
taller than the original AF-540FGZ foot. I put the whole assembly back together, hoping I could find a way to make it work, but unfortunately, the ground contacts (the two silver "tabs" on the sides) from the 540 are not long enough to reach to the bottom of the taller 360 flash foot. As a result, the flash doesn't get properly grounded, and no communication happens between the flash and the camera (the camera doesn't even see it there, doesn't fire, etc.)
Fast-forward another month and after saving up some $$$, I finally bought the 540 assembly and it worked like a charm.
So, word to the wise: If your 540 flash foot is broken, save yourself some time and just get the replacement 540 assembly.
A few photos of my learnings posted here:
Public Link:
http://www.facebook.com/album.php?id=502851915
Permanent Link (Log-in to facebook first, shared with "Everyone"):
http://www.facebook.com/album.php?id=502851915
For reference, hot shoe pinout is diagramed on this post:
https://www.pentaxforums.com/forums/camera-studio-accessories/54448-hot-shoe-pinout-k100d.html