Good to know he was in Gainesville the whole time, that means these were all issued there.
I don't know that the second stamp hurts your theory - I think it is possible that there might have been a little overlap in when consecutive series were on shelves, so having the cards over Piedmont 150-350 would allow for that possibility. Now, if they were 150s and 460s only you might have some bigger holes in your boat.
Who are the players on those 4 cards? According to T206 Resource, the 150 series was printed until July-August 1909 and then the 350 series started, but both of these were print group 1 cards. Print group two started in early 1910. So if all four are print group 1, then the possibility of them having been acquired at, or near, the same time still seems possible to me. (I am not a print group expert though, so someone else may have more to day on this idea.)