My early training was all in the Littaeur method - you learned to ride as a beginner on loose reins, using elementary aids, on a stabilized horse. Intermediate level was all about learning how the horse's body moved at various gaits and learning to follow it. You had to be able to follow correctly *on loose reins* before you were allowed to pick up contact. The end of this stage was jumping a course on contact with crest release. The next stage was learning active contact and using your aids in rhythm with the horses motion, and then, jumping with automatic release. My avatar photo shows an in-between, half-way between crest and automatic. GM would approve since I'm not using the mannered hunter ring crest release but would suggest I move on to a full automatic release.
The Littaeur lesson plans for teaching contact were a revelation to me as a young rider. My instructors had been alternately yelling at my for years to "soften my hands" or "shorten my reins" finally, someone came along to show me what they were talking about and how to do it.
Wished you lived near me; I'd be happy to share!
If your horse is really confirmed in his way of going, it might also help you to ride some other horses where the head and neck motion is more obvious and where you feel like you can drop contact without him scooting off.