Sorry, there are too many posts about 3/4 tons unhappy with handling of TT's. Obviously, a heavier 3/4 ton will not wiggle near as much but even your truck would be more stable with a 5th. You didn't say if you've ever towed a 5th or not?
I may have had a really poor TT compared to others. It was 11'5" tall, suspension was light enough that when we put out the slide, it would tilt a few degrees (our 5th does not, even when still on the pivoting hitch). But, I know for a fact there was over 1000 lb of tongue weight of 7000 total, a tight Equalizer hitch and towed it with the same truck we have now. Absolutely no comparison in stability. This is also just physics. And, for reference, our old GMC 1/2 ton moved around about 5x worse than this F150HD in bad wind with the TT. Same setup, hitch adjusted to get about 80% back on the front axle. I did have to lower it 2" on the shank and take out a washer because the hitch in the F150 is so stiff it doesn't flex.
There are never any comments about stability on the 5th forum but it's about 1 out of 5 for TT's. We don't need any other proof. The worst day towing a 5th is still better than the best day towing a TT.:)