You're making me soo jealous. This is the first year we haven't been to Gatlinburg/PF since 2005. =-p
Food City on 321 is your best bet if you're actually in Gburg. Just try not to think too hard about your stockpile at home.

There is the Walmart in Seviervile, but it is CROWDED. I only went there once.

The Kroger in PF on Wears Valley Rd wasn't too bad far as crowded. I'd just aim for ads.
Just try to remember (I tell myself this also!!) that you're on vacation. And ENJOY! I LOVE LOVE LOVE LOVE LOVE that area.
ETA: There is an Italian place in the same parking lot (across the gas station section) as the Food City on 321 in Gburg that is soooo very good. I mean, seriously good. You should check it out while you are there. :)
PP...I didn't know about the Save-A-Lot! Thanks!