While that trot looks pretty, it's not correct.
He needs to be driven forward into an active and correct trot. Allowing him to do a fake, forward passage is only teaching him to disengage behind.
I would like to actually see the side reins up higher, but not too high. They should attach to the billets just under the saddle flaps, and eventually up just about 4-6" higher than that, but no higher. And they should also be a bit shorter, and the inside rein should be shortened a great deal. The horse should be clearly flexed to the inside (this will also prevent the fake passage stuff from happening) and the reins should not "flap". Also once he is driven more forward, it will be possible to half halt with the lunge line a little bit. Again, the lunge line should not be flapping, there should be a contact.
It is also helpful to have a knowledgeable ground work person help you with the lunging to avoid some of these common errors. However you are doing better than most!