As was said, DO NOT DO THIS!
Here's why....
The specified shell length is of the FIRED shell. IOW, a 2 3/4" shell is only that long after firing. Firing a shell longer than the chamber means it will not fully open, and pressures will spike.
Shotguns have the same working pressures as WWII grenades, I'm told.
Unless you suffer from excess eyes and fingers, stick to what the gun is desgned for.
I like 311s and have owned a couple. But, they are great 2 3/4", reasonable loads shotguns, not Ubergun....