The old Tundra's EPA matched Fuelly... but all other trucks are way shy of EPA, and I suspect the new Tundra will be also. Maybe 15% better, 16 mpg vs 14 mpg, overall, which is what the F150 3.5 gets. YMMV. That's with no load. The turbos can get thirsty with a load.
1st gear on the Gen 3 is lower than the Gen 2 with its 4.30 diff ratio. And you have 10 of them, rather than 6. And more torque. It'll get around fine with 35s.
You'll be way over payload. I suspect the camper will be a lot heavier than you think... manufacturers of those lie like crazy. And you have not actually made a list of all the stuff and added it up. Just in suspensions and tire upgrades you'll gain 200 lbs. I wouldn't worry about that, but staying under axle ratings is a good idea. The rear axle has lost a lot of beef, so I think you'll want to load up your rear seat.
Stopping? When you really need to stop, traction with the road is the limiting factor. Surely the brakes are stout enough to enable ABS? Otherwise better brakes just allow you to get away with dragging them on long descents, which is something you don't need to do.
Hybrids are good for unsteady loads. Seems that might be helpful offroad, but I've never seen anyone test it.
As others have mentioned, 1st year vehicles are going to have more issues. If you like Toyotas, last gen would be a better bet. There's 15 years of experience with that one. A 1 ton would make more sense.