He's on the forehand.
No bit will fix that.
And any horse can be on the forehand, it doesn't have to be a TB ;)
What level of rider are you, and how much training has this horse had?
My response to how to solve a downhill canter will vary on the training. On my current horse who is training medium level Dressage, I able to ride an octogon shape in canter, instead of a circle, and think of riding a 1/4 piroutte at each point. It usually takes two pirouette moments for him to lift his shoulders.
If a lower level horse that is plain out on the forehand - you need to get his trot off the forehand first. Millions of transitions, changes of rein, leg yield and shoulder fore. The more you can change up the gait, direction etc. the more your horse will need to weight bare on his haunches, to prepare for your requests.
Trot-canter-trot transitions, and trot-halt-trot transitions are particularly beneficial.
The bit won't do a thing. You cannot bring a horse off the forehand by pulling on his mouth. Think of it this way - pulling back on the rein, pushes the hind legs out backwards. Riding the hind legs forward, pushes the head and neck out, thus reaching into the bridle and lifting the wither.