I concur, mushrooms would be an obvious choice. Personally I would make the dish a little simpler, but along the same lines. I find that complex food is somewhat distracting when I have a very complex wine. (It must be good food though, and as a corrolary I like simpler wines with more complex preparations.) Maybe omit the stuffing and the tomato.
Avoid vinegar in any marinde, even balsamic just to be safe (a little is fine though). If you use cheese, go for a mild to medium flavored hard cheese like parmesan or peccorino, and buy a small piece of the best one you can find.
Your wine is fantastically rare and special. I recommend making this dish a couple of different ways first and pairing it with decent ($25-$40) Medoc or Margaux wines to make sure you have a winner; they will be close enough approximations to yours that you will at least be able to get a feel for whether this dish works for you and this type of wine. Unless you are very lucky, wines like this are a once-in-a-lifetime experience; a little advance testing will ensure a perfect match.