You probably have a horse that is either trained for or bred for (or both) WEstern type movment. So, you have to work against that. YOu say you want a consistent forward trot, AND you want his head and neck down.
If he is trotting too slow, not engaging his hind like you want and too much on the forehand, you don't want to try and achieve both of your goals at the same time. You want to get him going FORWARD! First, without any regard for his head or neck position. You have to get hi to change his idea of what a trot means.
You don't want to push him too hard out of his natural rythm, but you want him to be working on acceleration. Acceleration is when a horse will reach under himself, and like a speed boat that acceleratest on the water, the front will lift naturally.
So, do the hillwork (which is also a form of acceleration because the horse must add force to go up), and do walk trot transitions and make sure they are prompt and vigorous, and don't fiddle with his head when he goes forward just ride him forward until he wants to quit. Let him , then go for another break-out forward acceleration.
Once you horse has more forward, then you can concern yourself with your rein contact and how and where he carries his neck.