First time I've ever heard someone complain about the horse coming onto its haunches in a downward transitions! I'm still working with my elementary/medium level Dressage horse to establish a downward from canter that stays over the haunches EVERY time!!
You WANT the horse to 'sit' in the transition, rather than dump on the front legs - you've got a very good horse there if he actually is sitting behind rather than dumping in front.
The thing about canter, is that once it's gone, it is gone and very hard to bring back. With an unbalanced horse such as this one, do not canter for more than 1/2 a 20m circle at a time. Work hard at response to the aids at walk and trot, make sure you have got perfect stop, go and turn buttons, and start some leg yielding and shoulder fore on a circle. The better the trot is, the better the canter will be. If it takes 5 strides to make a transition to walk from trot, it will take 10 strides to make a transitions to trot from canter.
Avoid cantering straight lines - straight lines are a horse's best friend - they can grab the bit and tank off. Stick to a circle for now. Ask for the canter by leg yielding towards a 20m circle off your inside leg, in trot. At about 18m, cue for canter, sit nice and deep, long legs, toes up with nice soft hands. Canter only for 1/4 of a circle, then calmly ask for trot and go back to leg yielding in and out on the circle. Change rein if he starts rushing - ride a figure of 8 or a snow man figure with gradually decreasing circle sizes, leg yielding out etc. until he settles again.
Once you've got a brain back, ask for canter again.
Rinse. Lather. Repeat.
Don't work solidly on the canter, just sprinkle it in when you feel that he will canter off nicely, without barging away. ONly a few strides, so that he can't grab the bit and run off with you.
Remember that as soon as you've lost him in canter, that's it. Fix the canter, by fixing the trot. The canter will only be as good as the transition, so make sure that trot is soft, forward and on the aids before even thinking about canter.