I have one that looks suspiciously the same from  the 30s.  I want to say it’s branded western auto.

I wouldn’t do it.  They are kinda poorly built.

Probably a "trade gun" made by Crescent Arms,iirc, for someone. Think you would best served by buying/trading up to a 3" gun.

Many times with firearms taking a particular model and throwing some work or money into it to try and make it different from what it is is just not worthwhile .

Sometimes this can be as simple as refinishing and never having it be worth money invested.

To rechamber a old somewhat unknown strength/condition shotgun strikes me as a fairly big gamble .

Steel quality and heat treating were kind of wild cards back in this time period. There were some improvements during WW 1 but there would be a lot of unknown stuff going on here in this case.

Is it actually 2.75? some of the guns from this era were less than 2.75" . Shells might fit in the short chamber but the crimped part of the shell doesn't have clearance to open properly causing a partially obstructed barrel and crazy high pressure .

My point is money might better be spent buying a gun that is set up to do what you intend .