I am by no means an expert in this category...
I own a 2013 F150 FX4 5.0 V8 SuperCrew. I am very happy with this truck. I actually chose this over the Eco boost. The FX4 with all the bells and whistles actually knocks off about 400 lbs in payload. Had I known about payload and everything when I purchased the truck (and the importance when towing), I would have more than likely spent more money and gone with a 250.
With that being said, I tow a 27 foot 7000 lbs (fully loaded) TT. Three dogs, wife and baby. With minor things in the box (stroller, some firewood, a few dog things) we are loaded if not maybe 50-100 lbs over payload (never more than that). Everything else, we throw in the trailer if need be (cooler, jugs of water) and let it do the work. I've gone over the math and figure that we are slightly over payload and at our max for towing.
I know the OP has already heard it a hundred times, but I personally wouldn't put any more pressure on my truck than there already is on it. Living in Calgary, most of our destinations are through foothills/mountains, so I am always conscious of where I go and what I bring.
Like some have said, it is definitely doable, but at what cost? Even our combo, we prefer to stay close and drive flatter terrain, but we do make one trip down into Osoyoos every year. Costs a fortune in gas, but always worth it.
I would agree with going a bit smaller for the floorplan you are looking at. Hopefully everyone here didn't stress you out over your purchase, probably won't hurt to make some upgrades if you have the cash.