I still think your horse has normal back conformation and what you have is a saddle that just simply doesn't fit this particular horse.
He honestly looks like he would be an easier horse to fit. He's not overly wide, doesn't have a sway back, a short back, etc. His nice withers will hold most saddles in place.
Why the Tucker doesn't fit I have no idea. But getting a saddle that fits is a lot more complicated than simply getting a wide or regular tree. Saddle makers want you to think that because they want to sell saddles. "Our saddles come in wide and regular, so it will fit your horse." Like someone else said, that would be like going to the store and buying clothing for yourself marked "wide" and "regular." Sure, it would fit a lot of wide people and regular people, but who determines what is wide and regular? And what if you are a small? Have a big chest? A big belly? Long arms? You might have difficulty finding a shirt to fit.
Your horse looks like a very pretty Paint to me, probably with some Thoroughbred in him, which is common in stock horses. I really don't see gaited or Arab, but who knows.
Actually, I own a QH/Missouri Fox Trotter cross with one hind leg shorter than the other! He is coming 3 years old. I *think* he has a gait, or at the least a very nice fast, smooth walk right before he goes into a trot. But I'm pretty sure he has a gait in there. I haven't really worked on developing it yet because right now he is a green 3 yr old that needs trail miles. But anyway, I own a cross like that.
Anything is possible. Your guy could have some gaited blood. But just looking at him, I see Paint with perhaps some TB breeding (which would still make him a purebred Paint if he were registered as such).
Unfortunately I think your Tucker saddle just doesn't fit him.
I disagree with the folks that say it's how you mount. Yes, if you hang like a monkey from the saddle horn you can turn your saddle. But I am a heavy, ungraceful rider. If the saddle fits I can still mount my horse most of the time from the ground (at least my short horses, lol). If the saddle turns easily when mounting I think it is a fit issue with the saddle.