Excellent job in the last line of the last vid. You corrected the rushing quietly. Very well ridden. The only other thing I really saw is he tends to go on to his forehand after the line and dive into the corner (and for some artistic flair a few crow hops). At this point you are still in two point. With a horse this green, you want to be back to your flat position, actively riding him in that corner, weight to your outside and inside hand raised, encouraging a bend and less diving/running.
Really he looks pretty good if you don't jump often and is obviously naturally athletic. He has a good natural eye for fences.