Charcoal and lighters are available at the store at the Fort. If you are checking bags, $store gloves, dawn, grill scrubber, matches, napkins are a smart buy. Pick up a scrubbable tablecloth for the picnic table and a pack of clips to hold it down while you are there. A box of foil wrappers will be handy.
If you grill chicken, for instance, cook extra so you can make chicken salad or chicken fajitas the next day. You can prepare grilled cheese sandwiches (add precooked bacon?) butter the bread and wrap in foil wrappers and then toss on the grill for a quick lunch. You can do the same with pasta sauce and mozzarella cheese. (Old camping recipes). I would cook a box of pasta for macaroni salad and have green salad as well. I would not bother with this much cooking at any other villa, but here with the grill available it is a chance to eat well and save $$. The trick is planning exactly what you need for food so you are not wasting most of it, but it sounds like you plan on cooking.
The Fort is quite spread out and has a bus system. You can rent a golf cart. Rentals are pricey, but a 24 or 48 hour rental would get you to the store for groceries, a few trips to the pool, a ride around the Fort and maybe even a quick load of laundry in addition to getting to the dock. Bring a bit of ribbon to tie on your cart so you can quickly identify it in the sea of matching carts. I'd trade a fancy sit down dinner for a 48 hour golf cart rental any day!
Taking the boat back from MK before fireworks is the best option IMO. You can then watch fireworks with piped in music from the beach and then hop in your golfcart for a quick ride back to your cabin.
Enjoy!