You've got a mind for the math and a good understanding of how things interact, but you are making too many baseless assumptions.
Everybody, without exception, is shocked when they find out that they are much heavier than they thought they would be. Your guesses at weights are almost certainly hundreds of pounds low as a whole. Camper dry weights are almost always a "lie." The manufacturer has boilerplate protecting them, an asterisk next to the number indicating that is the weight of a base model camper. Options and differences material density can make them much heavier. Few manufacturers weigh each unit as it comes off the line.
Then there is the distribution of the campers weight across the axles. Unless you sat down and did some basic beam calculations, you are taking a huge leap of faith there. For all we know it could be 1500lbs on the front and 300lbs on the rear.
People have done what you're proposing, and it was "Just Fine(tm)" for them. Be aware that this is one of those "ragged edge" things, and it takes a certain mindset to be happy with the results.