I've heard other people complain about flies at Cape San Blas, and it really puzzles me.
For 19 months, I lived on the beach at St Joe Beach (Selma Street) and as well as
Gulf Pines (near Indian Pass, not far from the Cape) and
never encountered a bug problem.
I suppose you could try either of those two locations.
St George is nice, too. I dunno, maybe it was just a buggy time when you were there, and not so buggy when I was. Now, mosquitoes are going to be around, but usually they are not severe.