I sympathise with Hobie1.
Latest version of F150 has aluminium frame, shaving off a few hundreds pounds. A stripped down trim (5.0L, 2wd, simple cab, long bed) is indeed rated for 3270lb payload by Ford (second to last page of the brochure [1]). F250 payload starts close to that number (third from the last page at [3]) and goes up form there. I think the heavy duty did not receive the aluminium treatment (yet?), so that's why the gap is fairly narrow between them.
So temptation is strong! F150 has much better fuel economy (up to 24mpg) and acceleration (5.9 sec 0-60) than f250/350. They say that heavy duty is more of a tank, by comparison, not nearly as much fun to drive and not suitable as a daily driver. But then of course as others noted, you start getting into it, and adding 4wd, super crew cab, and payload drops to 2700lb. ??? That's before bells and whistles ???
But let's see if the math can be made to work still? Looking at the other side - Lance 650 (the smallest one they have [2]) is 1900lb wet, plus 200lb for options (a/c, electric jacks), we're looking at 2100lb out of our 2700 budget, that leaves 600lb. Me and mine will be 200lb each including personal belongings and food, so we still have 200lb left for other gear and for, well, any surprises coming from both Ford and Lance.
For their part Lance actually lets you configure the camper and they show you the complete configured weight, so it should give you a pretty good idea of what you're getting before you're getting it. Ford is not as accommodating, alas, so surprises will come for sure...
You could also shave off some weight: removing rear seats and the tailgate might save what, 100-200lb? Give up 4wd and you get back another 200lb.
It's very close, but it might just work out.
[1] F150 Brochure https://www.ford.com/services/assets/Brochure?make=Ford&model=F-150&year=2018
[2] Lance campers https://www.lancecamper.com/truck-campers/
[3] F250/350 brochure https://www.ford.com/services/assets/Brochure?bodystyle=Truck&make=Ford&model=SuperDuty&year=2018