There isn't any chance you'll be using a towncar service, rather than DME, to get to your hotel, is there? When we stayed at the Swan, we didn't have the option to use DME, so we went with Tiffany. They allowed for a 30-minute grocery stop at the Publix on ... Vineland, I think. We were able to stock up with enough groceries to last the week, with the exception of milk, which we kept in stock thanks to the Screen Door General Store @ Boardwalk.
I wonder which is the more economical option: using a towncar service rather than DME, or renting a car for the day? Might be worth a quick research...?