Alright, so I was out at the barn yesterday and we had such a good ride!
He started off wanting to put his head down, but I've found that if I just keep firm contact on his mouth (not pulling on him, fighting him for his head, or loosening the reins), he'll put his head back up, and then I immediately soften and praise him. It seemed to work pretty well. When we took breaks between exercises, I let him on a loose rein so he could stretch his neck and then collected the reins back when we started again.
He did very good. Besides keeping his head up, we're working on getting him more on his hind end & carrying himself better. We did circles in every corner and the walk and trot with serpentines down the long sides of the arena at the walk/trot. Then we did an exercise where we walk, halt, back up, then trot off for ten strides and bring him back down and do it all over again. We also did trotting poles so that he will learn to carry himself properly. He did very good with all of the exercises! We threw in some cantering here & there, he did his transitions well. Then I rewarded him by taking him out of the ring and walking and trotting around the barn yard. He was a very good boy!