I don't know if lunging would help (maybe, if you had her canter & tried to keep her slow on the line), but when you had her go into the canter, was she at a nice controlled trot? If so, at the canter I would try some half-halts. ;) Circles are also good for slowing her down.
Stopping and going. As soon as you can feel the horse push off its hind sit deep and pull back slightly, but drive with your legs. Im not a big fan of circles. I do half haults alot, I also do alot of picking my horse up with my spurs as well as picking his head up so he goes back on his hocks I let go of his head and I do a half hault. Rollbacks help alot too. Backing up then sending them into the canter out of the backup helps. Those are just somethings I have done.
Something else to think about: lack of balance or pain can cause the same thing. Possum, my mare, used to have a lovely trot too but as soon as she had to canter she would rush it all and not listen to the bit much at all. She was also having huge balance issues that I couldnt seem to fix which made her rush a lot as well.
I got a chiro out to her and a few days later when I rode her she was brilliant. She now canters sensibly and collected and does 20m circles and rollbacks without dropping her shoulder and taking off.
Just something else to add to the list of 'maybe' problems :)
I always ride a fast horse on a 20m circle at the canter. Ask for her shoulders to come to the inside a bit - keep her honest by reminding her not to lean her haunches in (use inside heel) - keep steady contact with the outside rein, and ask her to flex/give to the inside rein. Transitions are also a wonderful tool - and I would suggest that if you lunge her you do a lot of transitions. good luck!