Just because your horse is stepping up under himself with more impulsion and power driven through from his hindquarters doesn't necessarily mean his trot will be speedy. Throughout the entire trot work he needs to remember to stay underneath you, but still keep the forward impulsion.
Also, a bigger trot won't necessarily stress him out either. Actually, if you introduce him to the concept of stretching long and low over his back at a nice, forward paced stride you might find that the good stretch is actually more relaxing for him.
Don't be afraid of the forward- that's why our seat and legs and hands are there to half-halt and keep the horses energy circling back through the body and not running out the front end. When you keep the pace your boy does, his hindquarters are never engaging, they are just there, swinging back and forth like a pendulum. He never works it through his back. Example: the hollow and tense in his back when you ask for the walk transition, then he finally braces his front leg and stops. You want him to sit down under himself for that transition.
On the flip side, the few strides of trot that the video shows as you trot out from the halt are much more in the direction of the quality of trot I want to see from this horse- and he is even capable of way more.
So to sum up: impulsive trot does not equal speedy trot, Yes, the strides might be covering more ground, but the tempo and quality are all controlled by you the rider, and when you keep your aids consistent and clear, your horse stays relaxed and listening in the forward trot-nothing to worry about there. Half halts and near-walk transitions will be your friends- making sure to trot forward out of them to get the hq motors in action! Give him a pace and expect that he keeps it- no need for the ultra workout posting you are enduring-he needs to work hard too.
I say all of this knowing very well how capable you two are- you're a great pair! I'm quite excited to see how you progress because I know you will do it and be great- I can tell that horse has an awesome stride in him.. somewhere.
Keep up the good work!
We are not human beings having a spiritual experience. We are spiritual beings having a human experience. -Pierre Teilhard de Chardin