You got it. Instead of mounting the trim directly on the door creating the problem you have pointed out in your picture, just mount the trim to the interior of your room and extend the acoustic panel on the theater side door to be flush with the edge of the door. If this acoustic panel build-up still gives you a problem with swing clearance, you could add a very, very slight bevel to the edge of the acoustic panel to fix the problem.
This may go without saying, but I would absolutely saturate the edge of this door acoustic panel and several inches in from the edge with fiberglass hardener to give a bit of durability. Because you know for damn sure people will be pushing on that door to get out. I know this next suggestion may ruin a bit of the stealth look you are going for, but you may even consider having a piece of finish carpentry act as a "push" plate on the theater side of the door to save the acoustic fabric from greasy snack hands and oils.
Edited by TMcG - 7/13/12 at 6:28pm