My Dad's Rem 1100 won't do it.
My 35-year-old 1100 will do it just fine. Rem-Oil (really thin and non-fouling) may be part of the reason. Are you using thick oil on your semiautos?
You may need to strip and clean it thoroughly, and replace the O-ring and maybe the pistons, at this point. I don't know how old it is and what it's been through. But once it's working, it should keep working.
I use gun wipes occasionally. Once in a while I wipe down the outside of the mag tube (where the piston rides) with a Rem-Oil Wipe from Wal-Mart, before I wipe out the receiver with it and run it down the barrel with a stick a few times. Apart from some grease on break-actions and a judicious drop of oil here and there on repeaters, that's all the cleaning I do to any of my shotguns, until I'm ready for an occasional "real" cleaning session in the back patio.
If I don't need lubricating qualities, just rust prevention, I like Bullfrog Gun Wipes a lot. If I want a little oil, I'll use the Rem-Oil wipes.
Any of the Remingtons and Berettas that have dominated the gas-operated shotgun market, as well as the less-common but much-loved Brownings and Winchesters, should shoot a case without cleaning -- assuming you only mean fouling. If you get the things full of mud, sand, excess gun oil, etc., a lot of guns get funky, even pump-actions. And Benellis are known for infrequent cleaning requirements.
(I'm guessing a rechambered AK probably isn't the best choice for you if you have an 1100 and an A500).