^^ a respectful horse and a relaxed one at that should slow their roll and drop their heads.
I use clinton anderson methods to help me with horses that have crazy gaits and need to slow down. I "cruise". To do that, you hold the reins in one hand and rest your hand on the horn or something so that the reins are loose. You tell them to walk. Let them walk wherever, DO NOT steer them. As long as they stay in the walk, let them do whatever. Do this for all gaits but probably not galloping. I wouldn't do it faster than a lope. If the horse slows down, ask them to speed up AFTER THEY SLOW, let them commit to their mistake. If they speed out of the gait, on rein stop them and begin again. Be patient, let them learn.
Soon after you do this a while, your horse will relax and slow their gait, lowering their head. So just put miles under the horse's feet for a relaxed headset/gait. I like to let the horse have thier natural headset, I do not try to lower in myself. However, I don't want it way high either, I just want a respectful position.
As for the neck reining question, I think the other answers are good. It just takes time, but it is definitely not a hard thing for them to learn or for you to train.
I got summer hating on me cause I'm hotter than the sun. Win-ter hating on me cause I'm colder than ya'll. I'm being hated by the seasons so forget ya'll who hating for no reason!