I'm no expert but I've shot a few rounds through a shotgun and some of the autoloaders won't cycle with 2-3/4 loads if they're chambered for the heavier stuff. My SIL has a Benelli clone from Stoeger with their current rotating bolt design and it will not cycle with anything smaller than a 3" mag load.
I've never needed anything larger than 2-3/4 for my needs but then I won't go after goose or high altitude dove either. Turkey are better hunted with a golf club out here than a shotgun. I've never seen a turkey while hunting but they're crapping all over the golf courses...
On the last Gun Nuts episode Phil B did a new gun test of the Rem Versamax.
It cycled everything from 3 1/2s to pink 1 1/8oz clay loads. The gas is not bled off at the mag ring on the barrel like my 11-87, it is bled off in the chamber.
The longer shell covering up more ports so less gas is bled off to cycle. The 3"leaves more ports open and 2 3/4" shells leave even more open. I would worry about this new gun like I worry about any new release though....
As for the turkeys, may I suggest a 5 iron?