OP, was that 04 a short bed or long bed?
If short bed, I haul essentially the same camper on the same truck. Long bed would put some of the weight on the front with a 811 and be better, but you're smart in figuring your tolerance for sway.
FWIW the setup in my sig on OE alloy wheels and 3700-3900lb rated tires has hauled the camper many miles on and off road, dirt, rocks, gravel bars in a river, cross winds in the prairies pretty admirably. (For me. Yes a dually 3500 or larger would get rid of more sway and have more factor or safety in the wheels and tires, admittedly.)
And YES if I was full timing or used the camper a lot I'd have a camper that size on a dually. But I've got only maybe 10,000miles of hauling the camper since 2013 and the camper only leaves the shop once or twice a year. The other 50 weeks a year a dually is totally overkill for me.