For starters it's inadvisable to have one's weapon in battery UNLESS one is poised to shoot while training, practicing, hunting game or varmints, etc. Having a weapon in battery should never be regarded as a casual thing, it's a setup for a negligent discharge. Even highly trained cops have been known to have a negligent discharge because they forgot what condition their weapon was in. I'm extremely deliberate when having a weapon in battery, and I never leave a long arm in battery when not immediately in my hands or momentarily set down. My loaded semi-auto pistols (i.e. in battery) are always holstered in a level 1 retention holster if not on my body and the revolvers I have loaded are holstered and out of reach except for my own access. For me my holstered handguns = loaded, ready to go bang when you pull the trigger. With a modicum of training it only takes a split second to bring a Benelli semi-auto shotgun into battery, so there's really no advantage to keeping a round in the chamber as much as possible. And if doing social work one is definitely not going to be wandering around with a round in the chamber, that's simply a disaster looking for a place to happen. Be safe. As for 3" rounds, that's just a waste of magazine space to gain 3-4 pellets over 2 3/4" shells, e.g. one can get equivalent velocity or better out of Federal 12700 or Black Aces 00 buck both in 2 3/4" shells. There are other reasons for not using 3" shells.
If you're interested in upping your capacity on the shotgun then I recommend using a shot shell card on the side of the receiver and a stock sleeve that holds 5 rounds, that combo has the potential to give you up to 17-18 rounds total in/on the shotgun (if a five round magazine) the moment you pick it up. In a storm you're just going to grab your gun and join the party, in exigent circumstances there's no time to be screwing around grabbing other stuff to suit up with, you're going to grab it and go, better make it as good as possible.
Again, DO NOT treat a long arm (or any arm) in battery casually, ever.