Interesting. My Alu Cabin on my Tundra, loaded, bed built out, etc.. comes in 200-400 lbs below both axle ratings based on what I bring.
Don't forget you are comparing your payload to GAWR (Gross Axle Weight Rating) on level ground. Once the pitch of your vehicle changes and the center-of-gravity shifts the load placed on individual axles changes significantly. This must be taken into account for tires also and with them you must consider compound angles associated with vehicle roll.
That is true, my GVWR is over but under on axle WR. Probably just like about 95% of people on here. Almost impossible to stay under GVWR with a camper, in my opinion.
It's actually very easy if you take time to plan ahead and this is what the OP seems to be doing. In my case I created a list much like the OP did, added about 20% or so for margin since all those little things add up, and selected my vehicle after. Currently I am right around 50% of my available payload and my suspension, braking, cooling systems, etc. are performing nominally.
The payload is why I switched to a 1 ton. I started with small trucks, went to 1/2 ton then jumped to 1 ton long bed. I travel in Baja and Mexico and went with gas, easier parts and getting it worked on. I don't pull anything.
Despite really wanting a diesel engine I too was convinced that a gas was optimal for my situation. Strike one - first I ran the numbers and a the break even on a diesel is around 250k miles - you don't begin saving money until that point and then you are pocketing a few pennies at a time. Strike two - my plans include central and south America where there is no ultra-low sulfur diesel. Strike three - the lack of support (tooling and knowledge) for modern diesel with Tier IV emissions south of the boarder.
A business owner I know summarized it best - he said that unless I was towing 15-25k daily and making money doing it, I had absolutely no need for a diesel and that my gas engine would be just fine. After two years and 55k miles of travel, some in Colorado, I can confirm he was correct.
Based upon my understanding of your plans - my recommendation would be for a gas powered 1-ton truck with 35 or 37-inch tires, an on-board air compressor with 4+ CFM at 50 psi, and a nice 12k winch up front. A gas 1-ton "should" have a 4k+ payload which places you right in the middle - this is where you want to be. The tires and compressor will dampen your ride on rocky trails protecting you, your vehicle, and everything in your camper. The winch will pull you out of anything that a suspension system, lockers, and big tires, are unable to.
Yes, I am partial to a 1-ton AEV Prospector but there are many other fine choices available. It just felt damn good to spoil myself for once after decades of dirty, dangerous, and sometimes deadly, work. I met with AEV, picked out my build, had my bank wire them money, and flew up a few months later to drive away in an awesome adventure vehicle.