JMO but I think you would be back to where you started, that is you weren't comfortable towing 11,000 with the F250. I towed 7300lbs with my 2010 F150 5.4 3.73 Max Tow. It did OKAY. When I moved up to my current 2012 Ram 2500 CTD I saw the light. It was so much more comfortable towing. The TT used to move the F150 a little sometimes. Never white knuckle but it was obvious that the F150 was not 100% in charge of the trailer. I was using an EQ 4pt sway WD. I did at one point install a used Hensley Arrow. That made a huge difference in the towing aspect with the F150. Did nothing for the whimpy 5.4 though.
Point is if you decide to got the F150 route I would invest in one of the premium hitches like a Pro Pride or Hensley Arrow. The 3.5 EB has great torque and should pull that load just fine. It's the stability factor that you'll give up.