Look at the frame of your trailer compared to the frame of the truck, big difference. I have no data to back it up, but when you go to putting heavy tall loads on the bed of a 1-ton truck, when you take corners my butt tells me it’s sketchy.
Side in campers don’t weigh squat compared to a machine tool.
Just about every class 8 tractor/trailer you see on the road is hauling more weight in cargo than the truck and trailer weigh empty, so that number is irrelevant. As long as you have enough engine to pull it, frame and suspension to hold it up, and enough brakes to stop it you are fine.
I don’t know where the “ton” ratings for trucks came from. I can only assume it was from a time when said truck were only rated for that much in the bed. Even today though a 150 or 1500 trucks is considered a 1/2 ton, a 250 or 2500 a 3/4 ton, and a 350, 3500 a 1-ton. The GVW has been going up on all the models across the board throughout the years though. I remember for years a 3/4 ton truck had a GVW of 8,200 lbs, my 2024 GMC 2500 has a GVW of 10,500 lbs. Then GM used to have what they called a “heavy half”, which fit in between the 1/2 ton and 3/4 ton models.
To the question at hand, could you haul a top heavy load at or near GVW, probably. Should you, especially noting that you do have a suitable trailer available, no.
Just seems like a whole lot of trouble to keep from having to hook to the trailer.