You need a bigger truck - it's just that simple. Even *if* you could get it to move, you won't like how it accelerates, how it pulls up steeper grades and how it feels at speed on highways.
When we bought our current 6800 lb TT, we sold our F150 and got a V10 F250 with 4.1 gears. The 3/4 ton truck is amazing and a huge step up from the 1/2 ton. It's so much beefier all round. Until you have or try one, you won't know how much better a 3/4 ton truck is. We once towed a TT with an F150 that was at it's tow capacity limit and it was AWFUL in every way. I'll never forget going up Grants Pass in OR on the shoulder along with the semis trucks at 35 mph with foot flat to the floor...
Order that new truck before sundown tonight and report back tomorrow... :)
Ps: If you you don't absolutely need 4WD, get 2WD.