Also, I find the more I push him forward into a long and low stride, the better his headset gets.
Head/neck isn't as important; you want the horse's spine to round up. Therefore beginning to carry himself. Reins should be long enough that they aren't death-grip tight, but not terribly loose either.
YOU have to be loose, and ask for forward forward forward. (And I don't mean rushing off like he's being chased by tigers.. he needs to be forward in a controlled manner. Use your seat to control that tempo.)
Push him forward, follow with a nice loose seat, not bracing against anything.
As Kayty said, ride your horse properly, when he's set up properly, including a half halt, transition him to a different gait ( or a figure.) Prepare him again, and transition him back down or change direction. Keep balancing him and sending him forward.
Throw "collection" out of the window, right now. That comes way WAY later. I'm talking years later, as many equine professionals in top ranks are STILL working on that.
When he's properly off the forehand you could stop and he would stop on the rear, not plow or drag or dig into the front.
It takes times and a good instructor is crucial as you aren't experienced enough to tell when they're put together or what you need to add.. YET!
And for heaven's sake, please be teachable. If your horse was doing all of this already, you wouldn't be here asking would you? I don't know it all, no one does. I'm willing to try and accept that maybe I've got some work to do.
Not just talking to the OP, by the way.