I would do the car. Either the location stated, or another hotel (the Hilton across from Downtown Disney has an Avis desk, for example, and most of the hotels in that area have something similar).
As for the stores, aside from the aforementioned (and definitely NOT recommended) Gooding's:
Winn-Dixie - Apopka-Vineland Road
Publix - Vineland Road (just past Orlando Premium Outlets)
Wal-Mart - SR535 near FL 536. Open 24 hours, but don't go on Sunday if it can be avoided. The shelves were bare in certain areas and it was jammed.