your horse has learned how to make it all stop. for one thing, you said, 'after a couple of quick turns". what do you mean by quick turns? When I have a horse on a lunge line, I usually don't want quick turns. are you perhaps using this method to stop and then 'quick turn' your hrose:
you stop moving your own feet, you step sideways back toward his hind end, and you sort of bend over a bit and look at his hindquarter, point the whip at it, and mentally push it away from you ? Does he then whip it away from you, bringing his head to a facing you position?
What I think may be happening is that for him, you are 'attacking' his vulnerabel hind quarter area, and he wants to keep that as far away from you as possible. He has also learned that he can stop and rest when he is facing you.
So, yes, you have to get his shoulder away from you and back out on the circle. But, once you do, if you put pressure on his hindquarters, to make him go forward, he will just swing that away from you.
To make him go forward, once he is position on the circle, you 'lead' him forward with some forward encouragement on the lead line. if you must encourage foot movement, put the energy at his real driveline, righ where the girth would go, right behind hsi shoulder. AND, if you put on any kind of 'driving' pressure, you must also have that clear forward pull on the line, and drop the driving pressure the instant he moves forward.
get it going good, and then stop for the day. you can increase lenght of time later. jsut get good clear communication and obediance first.