Geez. You were basically doing the same as towing a 5,000# trailer. I sure as *&^%$ hope a 6.0L with 3.73 can do that with ease. Heck, I have an 05 5.3L with 3.73 that routinely pulled 6,000# with ease
Most of conversations you read about the questionability of the 6.0L gasser revolve around pulling >10k# (double the equivalent of what you did). Heck, my FW wieghs about 10k empty and about 12k loaded and yes I would pull that with a 6.0L if needed but I would expect it struggle with it
Just some friendly advice here (its free so it is worth exactly what you are paying for it). Truck ~6k# plus camper ~3,200# plus ~200# passenger plus ~200# tongue wieght puts your truck at roughly 9,600#. Don't remember the specs for your truck but I imagine that is over GVWR (which I could care less about) but most of that load is on the rear axle, you might be exceeding rear tire or axle ratings. Go get the setup wieghed to find out.