Make your inner circle (the three tires) a bit larger, and allow yourself to actually walk a very small cirlce within it. You are almost spinning on your "inside" foot, which is practically planted in teh middle, as the outside foot steps around it. Becuase, I see you stepping backward, just astep, but it's still a body language that is uncertain and invites the hrose to think "slow" or "turn to the center", when you are trying to drive him forward.
When he doesn't canter at the 2nd time asking, "fall apart". Get really serious and smack the ground witht he whip hard enough it makes noise, and take a step toward his middle. Be VERY sure you do not step into his kicking range, but the forward push of your body and the increased whip action should push him to leap into a canter smartly. Then the next time, just a slightly raised whip and voice will do it.
When he is going well, lower the whip so it's almost dragging on the ground. Raise it for commands, and lower it when the horse answers correctly.
Upward transitions use an upward going voice, "Can-ter^" and downward, a falling voice "Tee- rot,"