I watched that last video, and when it started, I thought, "oh, good, a real trot/jog, not a wog." But, when he loped, it was not a lope. A lope/canter must have a moment of suspension, and that horse always had at least one foot on the ground. He was basically walking in the pattern of a lope.
I do appreciate Oh vair oh's description of the challenges one must pass through to achieve that. I could not do that, certainly not on a draped rein. I just hate to see the gaits slowed so much that they are no longer correct gaits. I also wonder if it doesn't , over time, kill the horse's correct natural way of trotting or cantering and create stiffnesses .