My load isn't quite as high as yours but I do put 2 ATV's above the bed rails. My 05 had airbags and a Hellwig anti-sway bar. The 18 is far more stable with the same load than the 05. I think it's a combo of the frame and the large overloads that are engaged in ALT.
Let me clarify what I'm saying on the air suspension against the older style suspension. On my 06 carrying a 4K camper the evolution of the suspension went like this.
1. No modification. I didn't like how low the rear set and it just barely used the overloads as the main leafs carried most of the load.
2. I added Air Aide Aircells. These replaced the factory bump stops just like Timbrens. Because the bumpstops set inside of the frame rails the camper sway increased. This is very similar to what the stock 18 factory air felt like; however I do think the 18 was a bit better controlled and it definitely rides smoother. Part of the additional fealingof control on the 18 could have been shorter sidewalls and duals though.
3. I then added the Torqlift stableloads that replace the bump stops for the factory upper overloads. This got rid of the sway while keeping the rear sag in check.
4. I felt I didn't need the air cells so I readjusted them to act more like bump stops. I.e. they were about a 1/2" above the axle when loaded so they would only come in on a harder bumps. This is where I ended with the 06. I feel the loaded ride was about the same as the 18 but the unloaded is better on the 18. This is the configuration that I said has better sway control than the stock 18 or any airbag only modification.
On the 18, since I didn't like the lack of sway control that inside the frame bags provided, I added a Roadmaster rear sway bar. (Slighter bigger than a Helwig Big Wig but my reason for using it was I preferred the axle mount better). The sway bar got the 18 up to the same or maybe slightly better sway control than I had in config 4 above. The shorter sidewalls and duals on the 18 over the 06 with 295/70r18(34") tires make it hard to be sure but it is good enough I don't feel uncomfortable on winding roads like I did before adding the bar.
Bottom line is the further outboard the load carrying is, the less sway the truck will have. In board air bags, especially if tied together to a common air supply (as opposed to separate inflation control on each bag) aggregate the sway all other things being equal. Simple laws of physics and moment arms.