Some people will never understand the difference between data listed for taxation and the actual vehicle capacities.
With heavy camper the load on your rear axle is going to be crucial.
You calculated 7000 theoretical load v/s 7200 lb tire capacity.
This is very small safety margin and slight side to side difference can overload one tire.
But the biggest error might come from initial calculation.
Don't see where did you get COG, but the site shows it a bit differently.
Usually short campers with small doors can have center of gravity close to rear axle, but long campers with big rear overhang have it behind rear axle.
That creates cantilever where weight of the camper takes the weight from front axle and adds it to the rear.
Meaning it can be that 4200lb camper will put 5000 lb on rear axle.
You will never know for sure without weighting each corner, but I think you are on thin line.
Good luck.
Edit.
Found the page with COG but although they say the fresh water tank moves COG forward, they "forgot" to mention how waste water is going to change it.
Waste water tanks usually are in the rear of the camper and I can only imagine how 500lb of waste water placed on very end of the camper can affect the load on rear axle.
