The difference I feel from English to Western riding is that one does less gripping with the thigh in a Western saddle and rides more directly on the seatbones, less dependent on the stirrup. To be able to do it well, you must be really loose in the hips to move with the horse. I dont' mean that English riders don't use their seatbones, but they do tend to ride with more leg /thigh contact and more of a grip through the whole leg, down into the stirrup.
Correctly ridden Western means staying really on your seatbones, not bracing into the stirrup and letting your legs hang down, ala bareback riding.
My guess is that you are gripping too much and this alone will keep you from being able to really get connected to the saddle via your seatbones.
That kind of unbalanced "fall" into a canter from a racing trot is very common for horses that are not well balanced, and/or the rider is leaning too far forward and unbalancing the horse.
Next time, when you ask for canter, sit back a little, think of "scooping " the horse with you leg and seat, scooping it UP and in front of you. Be sure you have a little bend to the inside when you ask, and keep asking for the canter if he trots. If he gets wildly strung out, bring him back to walk and ask again.