Is the shot in your 3.5 shells lead or steel shot?
Don't know your experience with shotgunning but other then something like goose hunting, never saw the need for 3.5 inchers. Unless of course you're just a recoil junky.
In most cases, when hunting(shot or slugs), you'll accomplish the same result with the 2 3/4 or 3" with a lot less recoil.
It will take some time/money but for turkey hunting you really need to pattern your shotgun with different shells to get the best load for your gun/choke combo. Again, other then a sore shoulder, I seriously doubt you'll find the 3.5" will out perform either the 2 3/4 or 3".