I second Cortana, hill work is very effective. HOWEVER this needs horse WALKING up hills, down hills. allowing horse to use his head and neck for balance. Not canter work or even trotting. Marching walk uphill is best. Bonus is getting horse used to being outside, looking and moving FORWARD instead of always seeing the wall or ring edge ahead to turn off of. Horse will enjoy the changing scenery too.
Other option is long-lining using two (truly long, 30-35 ft) lines. Horse is able to go BIG with you walking 10-15ft circles in the center, not just twirling there. You also need a whip with lash long enough to “reach out and touch horse” when he ignores vocal commands. Just needs a flick to enforce command to let him know you CAN reach him, mean what you say!
I suggest an inexpensive, 6ft stick, driving whip, then add lash length with parachute cord, put the popper on the end. What is sold as lunge whips are extremely top heavy, kills your wrist carrying it. They are made with too short of lash length. You can’t reach horse with a short lash, they laugh at you! Driving whips are light, easy to carry longer times, very flexible, can be pretty inexpensive. Witmer Coach Shop in Penn carries such whips in various stick and lash lengths. We drivers like choices! Ha ha
Couple other points; long lines have a LOT of leverage. Be careful how hard you are pulling as horse learns this exercise. Outside line needs to go around rump to help “control” the rear end, and is always run straight thru supporting surcingle ring to your hand so it releases quickly. Inside line also needs a surcingle support ring, never straight from bit to your hand. This support ring will simulates rein hold when riding. Both support ring should be midway down the barrel, so horse is less able to turn underneath the lines and tangle!! Once a horse twirls, you have LOST control! NEVER want that happening!!
Ignore any “drinky-bird” head bobbing for a while. Horse is learning self-carriage, has to figure out the most comfortable head position. You control the speed, drive from behind, which will cause changes in head carriage as horse changes his balance. We just ignore head and neck as they gain rhythm in gaits and SUDDENLY the head carriage is perfect for speed they go because it is the most comfortable place to be! I would expect to start seeing rmuscling esults within a couple months if done 3 to 5 days a week.
Long-lining can do a lot building/teaching a horse when done correctly. We never lunge horses, they are not learning anything doing that. Very few people know how to lunge a horse correctly. They are mostly chasing them in a circle, hanging on a line or rope. Lines are way too short, forcing small circles, horse pulling/leaning on the line ALL the time, rumps swung out. Neither will you get the desired results round penning. You are not controlling the body as needed.