If you rent a car and travel off property, mail your letters from anywhere but in Disney World. We had the same experience with friends/family not receiving letters till after we got back. Even Disney castmembers suggested it. If you don't have the chance to go off property, maybe you'll get lucky with a postal pick up. I heard they don't pick up mail every day.
But, I bought stamps at the store in AKL and also as you go into MGM on the right hand side. (Not sure what it is called).