Wow that would be scary, I hate it when you feel a horse is starting to take off on you and won't stop when you want it to, my heart starts pounding so hard. And well it just never ends well lol.

Barney sounds exactly like my friends horse. His name is Rhiszo. She just got him not too long ago, and at first when she walked him he was a pretty lazy horse, he was the slowest walker, but as soon as she got him to go faster he really wanted to go, and he was very fast too!

Right now I think she's trying to keep him below a canter, but if he does start cantering she tries getting him to stop by pulling each rein back and forth making his head swivel and if he doesn't stop to that, she tries pulling the reins back slowly and further until he slows down.

If that still doesn't work, then you could try putting one of those straps on him that hooks from the bridle to the saddle to keep his head down. I hope he gets better for you soon