nice work! Glad you could get a few strides to get the way it feels.
I often do it on the trail (since I do way more trail riding than arena work) and when I can only do walk rides (due to MY health issues, not the horses), I ask the hrose to really WORK when he goes up a hill. I do long and low UP a hill, at a walk. This really stretchs his back and makes him have to work hard with his hind end and push up that hill.
When I get him to carry the bit down and forward , as described , I then ask him to kind of (and this is my own visual image) "step over the rope". I think of the line from my right hand, down the bit, through his mouth, out the bit and back to my left hand , and over my shoulders back to the right arm , as kind of a "hoop", that I lower in front of the horse, , that is a few feet off the ground, and I ask him to step "through" that hoop. Of course, he isn't actually stepping over anything. But thinking of the bit and my arms as forming a hoop through which he energetically steps up and pushes through helps to get him to connect through his back to his hind end and stay connected to the bit and pushing. So, it is a true excersize, and not just him dropping his head from the wither and letting it hang while he meanders up the hill.