Not enough truck. 7400lbs dry is probably 8400lbs. Couple that with 31' and the TT weighs more than the truck and is overpowering it. When I towed a 31' 7300lb loaded TT with a 2010 F150 Max Tow I had the same situation. Lots of wandering but never white knuckle type. I added LT tires, SuperSprings and used a good EQ with 4pt sway. Had the front of the truck dialed in perfectly. But just the weight and length of the TT would move the truck a little. Always had to be glued to the wheel.
Moved to a 3/4 ton truck and all the glued to the wheel sensation was gone. Sure the TT still waggled around but the truck stayed solid. Side winds never fazed it.
Next move was to a 5th wheel. That's when towing got really relaxed.