That's exactly what I was suggesting.
The OP asked about minimizing the lean when he hits the button. The whole purpose of a sway bar is to minimize body roll without having a serious impact on ride. It's not as comprehensive a solution as air bags, but it's one that wouldn't require as much adjustment or maintenance.
I've used air bags in the past and have really liked them. The OP should just be aware that they will stiffen the ride some.
Anti-sway bar is great idea, thank you for the suggestion..