I have a few ideas,
1)Maybe you can buy your groceries ahead of time and ship them yourself.
2)I have had perishables shipped to me using next day delivery. The cost might come out the same between delivery fee and tip.
3)What about renting a compact car for a day, some rental companies have a drop off center at the resorts.
4)You can take a cab from the airport, just have the driver wait while you run in to buy some things. HTH!