Unless I'm just taking my horse from A to B, I use a rope halter and a 15 foot nylon lead, no chain. They really encourage duller horses to come off of pressure.
It doesn't sound like you have an equipment issue, though, more of a learned habit. I would carry a stick or dressage whip when he's being led, and when he decides to pop it in reverse, tap him rythmically behind his driveline (Just follow him backwards, keep the lead as slack as possible) until he comes forward, then rub him gently with the stick where you tapped him while he walks forward. If you have a cue stick, you can increase the pressure as he ignores you, but if you're using a dressage whip it's going to be more of an irritation tapping. Traditional whips are too floppy and can really sting if used the same way. Make the right thing easy and the wrong thing hard.
You may need to establish a personal bubble for yourself with this horse, too, if he's stepping on you or running into you. As you said, Piper, major groundwork.