Yep, chin chain will give you a bit more control in there. You could probably also attach the lines to the lower portion of the bit (near the spoon), I'd assume that's why it has sections down there. I'd also agree with Endiku and Greetree, he probably just needs more time and miles if your only problem is when cantering.
How does he do lunging and/or long lining at the canter? When I got my horse, he simply couldn't hold a balanced, steady canter. It took a lot of time trotting collected and only cantering on the lunge line before he had the muscles to be able to hold a canter with a steady rhythm. Now we are slowly increasing the amount of time cantering under saddle. I'm sure it's even harder when he's not only steadying and slowing himself, but also the cart, which at a canter has a good bit of momentum.