Its interesting to see this question posted. I flip homes, and I just bought an entire pallet of laminate flooring. The easiest way to load it was to lift the whole pallet into my truck. I estimated just over 2000 lbs, plus I had my wife in the front seat and other gear and supplies in the back seat. My work truck is a 2004 Chevy Avalanche, with the 5.3L.
The Avalanche is more designed for comfort than hauling, so it has a softer suspension than the 1500 Silverados do. The forklift guy loaded it slowly, and the truck bed lowered several inches. I looked before driving off, and decided it was OK to proceed with caution. Other than the bed being significantly lower than the cab, the truck did pretty well. The part that was a bit challenging was quick stops or sharp turns. definitley doable, but care was need to not just casually whip it around.
After getting up on the Interstate, the truck was perfectly fine. I did drive 70 instead of the usual 75-80, just for the sake of caution. So, considering your airlift suspension and lower gearing, if my 2004 Avalanche handled it, I think your RAM is definitely able to make it in one trip. Just take your time and avoid quick start, stops, and turns. Your RAM is very capable to do this.