Chamber pressures are not directly related to velocity in shotgun shells. Be clear on that. Go look at Hodgdon reloading site and look at loads for Longshot in 12 gauge. They will give very high velocity with much lower than expected pressures. Alliant 300mp, in the .410, is the same low pressure for high velocity type load. But just as in rifles, the fastest loads did not produce the tightest groups, the fastest loads do not always produce the best patterns. Nothing is free in ballistics. You trade one thing off for an improvement in another.
Shooting longer shells in short chamber increases pressures. Worse pressures in longer factory shells goes up by length. So your 2 1/2" factory shell might be 8k, your 2 3/4" might be 10k, your 3" factory shell might be 11k and your 3 1/2" shell might be 12.5k. If you get an extra 1k per different shell what coluld the effective pressure be if you shot a 3 1/2" shell in a 2 1/2" chamber? 15k or more. Who knows but nothing I'd be will to risk in my gun.
I thought that as well, that pressured jumped off the charts, but the link that Drew provided showed the jump from 2 1/2 to 2 3/4" in their short chambered test gun only went up by 500 psi. I expected much more of a spike then that frankly.
Here's what the results were copied from what Drew provided:
“Shooting 2 3/4” shells in 2 1/2” chambers does make them produce more
pressure-but in most cases it is less than a 1000 psi increase. I see no reason,
related to safety, to modify an original 2 1/2” chambered gun to shoot
2 3/4” shells, if the 2 3/4” load you intend to use would develop pressure
that is safe in that gun, when fired in a standard chamber!”
7. “We found that lengthening the forcing cone in a 2 1/2” chamber usually helps
mitigate the pressure increase that comes from shooting 2 3/4” or 3” shells in
the short chamber.”