the 3" measurement and the 2 3/4ths measurement are based on the shot shell after it has been fired and the crimp has opened up...
So you can load 3" shells in the magazine tube, and then pump them and it will fit just fine...but it will be hard to get out.
Also note, generally 2 3/4th guns are older and not made as strong. 3" chambered guns are newer and stronger, so the factory will load 3"ers more powerfully...enough so that YOU CAN BLOW UP YOUR GUN AND LOOSE SOME FINGERS AND MAYBE GO BLIND AND SCAR YOUR FACE UP NICE- note, this is a worst case scenario, and most guns are strong enough to handle a couple dozen of the more powerful 3 inch shells before coming apart, but I just value my eyeballs very highly, and my fingers too.
plus, the auto will have too much power and it will screw up the internal mechanisms and not feed the next shell right, aside from the fact that the old shell will still be stuck in there.
Note: TURKEYS CAN'T READ. they will be just as dead if you shoot them with a box of shells that doesn't say turkey on it. What do you think turkey hunters used before turkey hunting got so popular that specialty shells were used?
Get the biggest size lead pellets you can find in 2 3/4ths, and realize that you won't be able to shoot at birds quite as far away as the guys with 12 guage 3 1/2 inch shells
here are some good ones
Remington Express Long Range SP204, 20 Gauge, 2 3/4", 1 oz, 1220 fps, #4 Lead Shot, 25 Rd/bx
Federal Premium Game Shok High Brass H2044, 20 Gauge, 2 3/4", 1 oz, 1220 fps, #4 Lead Shot, 25 Rd/bx
Winchester Super X High Brass Game Load X204, 20 Gauge, 2 3/4", 1 oz, 1220 fps, #4 Lead Shot, 25 Rd/bx
OH LOOK AT THIS 20 GAUGE 2 3/4th TURKEY LOAD! I THOUGHT YOU SAID IT DIDN'T EXIST YET TYPING "20 guage turkey 2 3/4" INTO GOOGLE FOUND IT!
NOW IF YOU FIND TURKEYS CRAFTY ENOUGH TO READ THE SHELL BOX THEY WILL DIE!!!!!
http://www.midsouthshooterssupply.com/item.asp?sku=0009601275
http://www.ableammo.com/catalog/product_info.php?products_id=99451