I think that's what everyone is trying to tell you...it's not feasible.
I don't think you're understanding the loads you'll carry with that 865. It WILL be over 3000lbs loaded with people. Although you may find an f150 with a 2900lb payload, the GAWR is only 4800lbs. This means if you max out your payload at 2900lbs you also max out your axle. Do not do this. Many people exceed the payload but I haven't seen anyone willing to exceed the GAWR.
You say under the payload for any long bed f150. That is the max available payload with special configurations. Many of of the f150's you find on dealer lots will have a payload around 2000lbs.
2011 is the dry weight. The "claimed" dry weight with zero options as I said earlier. Every manufacturer I've seen underestimates the dry weight by at least 100-200 lbs. Air conditioner 80lbs, awning 40 lbs, solar panels etc they add up quick.
"Claimed" DRY weight of 865 you're considering (with no AC, zero options)- 2011
Propane, battery, gear, food and water for 3 people - 700lbs
Three people = 600lbs
Wet weight ready for a trip = 3311
An 865 loaded with gear and 600lbs of people WILL be over 3000lbs. Likely closer to 3600lbs for a longer trip. You cannot carry this on an f150. The 825 will only be 200lbs less than this. You cannot carry it loaded on an f150. Also, when they say sleeps 5 in the 865 they're not saying that they're all adults.
You could carry the Lance 650 on an f150 but it will be very tight for three adults. You can carry an Alaskan on an f150. There are a myriad of pop-ups you can carry on an f150.