http://forum.doom9.org/showthread.php?t=152419
Roozhou patched a version of ffmpeg so that it will demux the video stream, modify some of the video stream attributes, then repack it without actually re-encoding the video. It modified one of my files in less than a second, so I'm pretty sure it didn't re-encode the whole thing and loose any clarity, and when it was done, the file worked everywhere that I want it to.
It's still an extra step that I wish I didn't have to do, but it finally lets me put out a video in exactly the format that I want, and not be forced into 4:3 or 16:9 aspect ratio.
I never could find any real documentation on the profile.ini settings, so it's still possible that there's a way to tell PD to put out a file with square pixels regardless of resolution.