From the info that you have given us, I would have to agree with you that a newer 350/3500 SWR truck will be suffice. But like you said, a trip to the scales will tell you for sure. I would guess that the hitch weight would be between 800 and 1200#.
03 Silverado cclb 3500 drw, D/A, Reese 22k hitch
07 Alfa SeeYa Gold 30RL,2 slides,power everything