My guess is that he doesn't really understand to move off pressure, either leg or bit pressure. He may need reeducating on how to give to the bit, and how to move laterally.
Get off the rail and ride him in the middle and do lots of work bending him and asking him to step over sideways. YOu might even have to back down further and work with him on the ground having him give to a rope halter and move off your hand pushing on his girth area.
He isn't going to go like a normal 6 year old because of the lack of riding horse training, but you can fill in those gaps by going back to basics. If you don't, you will be riding a horse that really is stiff and resistant and not very controllable, and ultimately , that is a dangerous ride.