Well, I gave 3.6.10 a try, and from what I can tell it works with no problems whatsoever. All I had to do was stick the build in the TBP directory, run it, and I was able to play through the one coop multiplayer mission with no incidents. The only thing is that it connects to the 3.6.10 beta server daemon as it no longer uses fs2open_pxo.cfg, so it gets annoyed at the tables.
Here are the things I tested:
Intro works (that's really cool by the way, nice work. Makes me want to watch season 3 again).
Tech room works.
Interface: There seems to be a transparency issue with the game-type icons in the server list screen for MP, otherwise everything looks beautiful.
All in all, I'm pleasently surprised. Didn't try SP, so that may still have issues, but nonetheless I think you may have to start mentally preparing yourself for getting smacked with a gob.