I tow a trailer that is 28' coupler to bumper no issues. Can my truck tow a 34'? I have no idea never tried it so no point commenting whether it can or can't.

Like someone above said go to the 1/2-ton towing page on Facebook or even on this site under "lets see your campers", many towing over 30' with a 1/2 ton.
Lets see your campers being towed - Ford F150 Forum - Community of Ford Truck Fans

 

Seems like contradictory statements.

 

In answer to your original question, the discrepancy in that one source stated maximum capacity, NOT your truck as built capacity.
The truck sticker is definitive. The other matching source goes by your specific VIN, I.e., your build.
Opinion, mostly:
That particular 35’ trailer is HUGE for an F150. The weight, 7600ish GVWR, is only half your concern. There are a some F150s that have the capacity to pull that (like mine) but the F150s comparative light weight for a truck and also light for its size trailer means that huge side sail will blow you off the road, sadly.
You don’t mention your travel trailer towing experience. The weight isn’t bad but just getting near 30’ is not for beginners.
It’s also too long for a lot of length limited state parks.

 

There is about a 0% chance you'll be within all your weight ranges with that trailer and the people/animals/stuff you listed. That is also a HUGE trailer for an F150 to tow. Even if you somehow managed to come in under weight, that will not be a pleasant towing experience. My guess is by the time it's all said and done, you'd have close to 1,000 lbs on the hitch with that monster.

Beautiful TT and I'd certainly love to have that, but I'll have to wait until I upgrade to a 250/350.

 

Im guessing that trailer will have a 900+ lb tongue weight when that trailer is loaded up with all your gear. It might be 6000 lb dry, but with propane, batteries, second A/C if you get it, pots/pan, and all your stuff, its going to be well over 7000 lbs. 12-15% of 7000 lb is 850-1050 lbs of tongue.

Then another 200-250 lbs for your canopy? So you have about 400 lbs left for 4 dogs, 3 people and all your stuff. Probably not staying under payload.

That said, your truck is probably about as good as it gets in terms of an aluminum F150 goes. 157" wheelbase and a 5700 lb curb weight should help it be pretty stable.

 

If you carefully load the trailer, you can get much closer to 10% and still be safe. So even fully loaded you can be around 750 lbs tongue. I managed to get a 10k trailer just over 1000 lbs. You will be better off than nost with the longer wheelbase.

Lifepo4 batteries have come way down in price lately so that could save you up to 100 lbs on the hitch alone. Throw the generator in the very back (preferably propane so you can put it inside) and let her ride.

 

I suggest you "officially" weigh your truck full of fuel then you can guestimate the rest of the load available for your truck.
Also as a closing requirement of ANY RV I would make the seller/dealer give you an official curb weight from a local truck scale before signing a Bill of Sale or title.

I would also highly suggest investing in the following if towing often with a 1/2 ton:
-RAS
-high quality suspension (shocks) that has adjustable damping controls on the shocks
-proper load rated tires

The OEM suspenders are pure junk.

 

An F150 would tow that.. but you'll be miserable the whole time.

 

payload is calculated with a full tank of fuel

 

Yes, I plan to get the RAS kit. I'm not very familiar with aftermarket shocks though. If you have any to recommend, please do.

The truck also already has upgraded tires - we bought used, so I'm not sure if these came with the Ford FX Off-Road option shown on the window sticker, or if they were added by the previous owner. They are Terra Raider A/T-X KU-257, size LT265/70R17 121/118Q, M+S. Load range "E". 80 psi max.
Using charts or calculators like this one, it seems we should be normally inflating to 48 psi, rather than 35 psi from the door sticker recommendation. I'm wondering whether an even higher inflation would help when towing with a near-max payload though. Thoughts?