Re-reading this thread, I've realised that I hadn't taken the time to read Claire's post properly. I'd mistakenly thought she was referring to the Publix near the Lake Buena Vista outlets on Vineland Road (hence the reference to the Osceola Parkway and my confusion over the Outback Steakhouse).
I've just been researching via Google maps. According to that the Publix near Premium outlets is 5.8 miles from Pop, the one near the Lake Buena Vista outlets is 4.2 miles and the one near the Western Beltway is 3.9 miles. There's another detailed on the map between Gaylord Palms and the 192 on International Drive South which is only 1.9 miles from Pop. I know the area, but it's not one I'm familiar with. Checking the Publix website, it's known as the Xentury City Centre store.