You could try doing some Grooming and Showmanship with him. Like, walk and trot keeping his throatlatch at your shoulder and stopping with minimal pressure on the lead. Turns on the forehand and haunches, backing up, even setting his feet off of lead pressure. You can string the individual maneuvers together into a pattern for a challenge. I do this with my guys when the weather get nasty, and it keeps them from going totally stir crazy on me, and I have much better control on the next ride than if I let then veg out during bad weather stretches.
Also, on the softening his neck, you could try carrot stretches, or full blown lateral flexion to the halter or bridle.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown