I didn't really get a chance to dig into this last night at all, but on the surface I can't see why Sentinel wouldn't be picking up all 337 of your badges when you use /info_self. We do know that Sentinel doesn't always pick up badges as you earn them on the German and French clients, but /info_self does not rely on English/German/French names and should be universal.
From what you said earlier, it sounds like Sentinel is at least detecting the badges, though. When you used /info_self, did Sentinel indicate your badge count was 337?
If so, was Sentinel displaying your character's custom image on the left at the time, or was there text in there stating something like "Character not registered"? There have been some issues after the last game patch or two with Sentinel needing to be restarted if it's already running when you start the game up. After that it seems to be fine.