Hank, Think carefully about a single INFLATOR. If you want to inflate both bags with side-by side air fittings, that's a very good thing. But a common fitting, then a Tee to allow inflation of both bags, isn't a good strategy if you want then to help you with sway. When it goes to "wallow" you want the bag on the down side to hang tough, not transfer some of its pressure to the bag on the up side.
OP, Your word "Wallowing" continues to nag me. Unless your other car is a Porsche, you shouldn't be using "wallow" as a comparative to other vehicles' handling when you talk about a relatively small RV. I envision EXTREME sway, and it's hard to think there isn't something badly worn or damaged in the OEM springs or their shackles, etc. But especially on a Chevy chassis, that seems to handle a little better than a comparable Ford, "wallow" just doesn't fit, at least for me. By all means, the Hellwig sway bar will help. I hope it alleviates your defined wallow. If not, air bags might work, and speaking of Hellwig, a "helper" spring that kicks in when one side it goes to be the down side the helper on the up side isn't stiffening it. My guess... If it wallows as bad as the word Wallow implies, I think there's spring work ahead... And I hope not, just a couple mods will help you.
OH! I think it came up earlier in this thread, but don't underestimate your FRONT sway bar. If it already has one, spend a few dollars on hard plastic bushings for it. A Hellwig front bar would help even more, but getting the best you can out of the existing one might be enough.