I like the circles you were doing at the walk. I would also do those kinds of circles at the trot, encouraging the horse to push through the circle and drop his head.
I would also like to see more active engagement of "give and take". You seem to hold, hold, hold, with no guiding release whether his head is down or up. If he is just learning the basics of contact, you need to exaggerate the release a lot more. Hold, the minute he drops, release the contact entirely. Then pick up again. Otherwise he continues to get very brace-y as the end of the ride showed him getting worse than getting better through his softness.
I would also drop the reins completely at the lope until you have it through the trot. He's just bracing through the lope and not listening at all. Once you have him moving through at the trot better, I would do the same circling and pressure-release at the lope.
Cute little bugger though :)