Hrmm... I might suggest a different Publix.
Exiting out of the All-Stars, go underneath the bridge, and take a Left. Once on the Osceola Parkway, get to the FAR LEFT as if you're going to AK Lodge (NOT the park). At the traffic light, take a LEFT.
This road (Sherbeth?) will take you out to 192. Bunch of restaurants, shops, etc. At 192, take a RIGHT. About a mile or two down the road will be a Publix shopping plaza.