Hahahaha!
I know I was being a bit of a smartass and I hope no one took offense. But there is a bit of a point. Hoyt just reminded me of it.
I have never taken a turkey with anything more than a 2 3/4" 12 or 16 gauge shell or more than a load of 1 1/4" ounce. I have never wounded a bird and lost it. My occasional friend and turkey hunting professional here, Adrian Hare, hunts primarily with a 20 gauge. It's about choke, patterning, range and waiting for the right shot.
I don't have a 3" gun, never mind a 3 1/2" but Hoyt makes a good point....despite having the availability of the 3 1/2" load, he's rarely needed it. I would guess Hoyt knows what he is talking about.
Take the gun you have, find a load that patterns well within a prescribed range, learn to judge that range accurately in the field and shoot within those limits. Bang! Bird falls over dead.