Hey, my horses name is Ziggy too
Your first tip to me that this horse is being reactive is that his head is high, so his life is UP when he is going into the canter....this is not a good thing, as he is being (over) reactive to something, whether it's your cue or his emotional baggage from a previous experience.
Since you've started Parelli there is something you can look into that would be my first answer to this problem. In level 2 you will learn a riding pattern called the "cloverleaf" ask someone to explain it to you, and providing your safe there is no reason why you can't start it now. It's perfect for slowing down fast horses and speeding up slow horses. It's in the impulsion program of Stage 5 if you know any L2 students and can look at their pack, or ask an instructor to explain it.
My Ziggy (also a QH) prefers to canter over trot, as the canter is easier for QH's, (so I've been told) His has an elevated trot, which is unusual for the breed, and so if it were up to him (it's not though), he'd canter or walk. But with my Zig, it's never fast. The only time I see him go fast is chasing the pony away at dinner time, the rest of the time his canter is just a lovely lope that I could ride all day.
Here in Australia we find many conflicts between traditional trainers and what you are taught in Parelli, but the rewards are worth it.