You can get an F150 with plenty of payload capacity that will fit under your length limit. The one thing that might limit you would be the 1,220lb tongue limit with WD for the factory receiver, I can't find a class v hitch for the current generation F150 so that's going to be your limit unless you get something custom made.
I checked the Titan XD just to see if the other built half ton was a better option and it has the same 1,220 class 4 hitch limit, but there are aftermarket class 5 hitches for the Titan XD. Unfortunately at 230.5 inches it doesn't meet your length requirement.
It doesn't seem like there's a great option for a garaged tow vehicle for something that heavy.