Very simple - take an overnight bag with swimming trunks and change of clothes. Put the do not disturb sign on your Disney hotel, and come back in 40 hours. Why not just sleep there and casually enjoy the evening on Wednesday? On check out day, give your overnight bag to luggage services, hit EE, and when you are ready to leave, stop back for your bag and go back to Disney.
I think your desire to be back in Disney on Wednesday night is what is making the logistics seem more complicated. Also, we use a car service so we don't pay parking. From the time you arrive at the hotel to the time you get to the park is about 20-30 minutes, it is very efficient.
I have done this on 6 occasions and it works great. Granted, I have been there many times and I have a different perspective now, but an evening swim and sushi at Orchid Court is very relaxing. Personally, I have never had trouble at my "home" hotel. I tell them what we are doing, the do not disturb sign has been honored, and I have all of my valuables with me.