I've shot steel out of mine. Nothing larger than 2 shot. I use steel in 2 different 311's. One from the 60's and another from the 70's. What is bad that many of the 311's had full choke barrels. If your chokes are full try Kent bismuth. I reload and use some fast shells that have low pressures. 1 1/16 oz. steel loads that run 1675+ fps with pressures that are comparable to lead trap loads. Around 7600 psi -8200 psi. With 3s and 4s, it is a deadly load on ducks over decoys.
Back in the lead days I used to use 1 5/8 oz of 4s out of the 311 s and they would kick like a mule. But it sure was a killer on waterfowl.
The only problem that I see is many of the older 311s is that they have a tendency of having the stocks crack right at the tang when the shooter shoots a large quantity shells. I only shoot a box or two in a full season.
It all comes down to wether you want to use steel or something else.
Just did a search and found Bismuth shells that are copper coated for $30 a box of 20 shells. They come from Boss. A load that is 1 3/8 oz in a 2 3/4 inch shell is $28 a box. $1.40 a round which is cheap.