The SAAMI pressure standard of 12,000 psi applies to both the 2 3/4" and 3" 20ga. So other than the increase in pressure that would result from an overly long shell, pressure is probably not the main issue. But you'd be subjecting the gun (and yourself) to significantly greater recoil because of the heavier shot charge. Here's a comparison:

2 3/4" 1 oz, 1300 fps: 19.9 ft-lbs
3", 1 1/4 oz, 1300 fps: 31.1 ft-lbs

So right around 50% more recoil, assuming similar velocity.