SMB boots will not help with tripping , at all.
I used to ride a big horse that tripped alot. It was partly the way he walked, (he would rotate his hock a lot. You know, plant his back foot then pivot around it, so you'd see his hock moving kind of circularly)
And the other part was him not engaging his hind end and stepping under a bit more, and really being "present". I would pick up some contact and ask him to step up a tiny bit faster and bigger and step into the bridle, even when just out cruising the trails, and he tripped less. But, he always did trip.
My current mount will almost never trip, not matter how loosely he is ridden. He just is balance more on his hind and pays attention and picks his feet up, without any real encouragement from the rider.
Even though it may seem counterintuittive, make him move faster and bigger and he'll likely trip less.