I have shot a lot of the 3" Federal Mag-Shok shells with both 1.75 oz. and 2 oz. of #6 shot but none of the 2.75" shells.
It sounds like your gun has a full choke, according to your description.
I have found that the 3" lead shells do pretty well through a full choke, especially at the ranges your intending to shoot. I would think the 2.75" would pattern quite well at those ranges too but again, I have no personal experience with them.
I would really "deep clean' that barrel before you try them. Those wads seem to respond better to clean barrels, at least to start. You can find some guidelines at http://www.allaboutshooting.com
in the article "Cleaning a Shotgun Barrel".
You may also want to try the 2.75" Winchester turkey loads. They make a variety of shells with different payloads. I'd recommend that you stick to the #6 shot with your gun. It should flow better than the larger sizes.
I hope that helps some.