over emphasize your canter ques. Make sure your inside leg isn't touching him at all (from the knee down), and put your outside leg back a little farther. Don't just press with your outside leg, give him a nudge/kick with it. If you still have problems, push his haunches away from the rail, almost like you were going to do a haunches in, and then give the canter que, if will be hard for him to balance if he tries to pick up the wrong one, so he'll need to pick up the correct one.
One more thing that works for me with Intensity (he used to be able to pick up whatever lead you told him, FROM A STANDSTILL in the middle of the arena, but because of some people riding him that didn't know what they were doing, he is EXTREMELY TERRIBLE at picking it up to the left) is I trot him in a circle (less than 20m) and just keep clucking, telling him to go faster and faster, but remain at a trot, and keep that up for a minute or two, and then just push him to go faster until he has to canter. It sounds weird, but he picks it up correct, nearly every time that way.
I have to disagree.
Always, ALWAYS use your inside leg in the canter cue. You first apply pressure at the girth with your inside leg to bend the horse, then use the outside leg slightly behind the girth to emphasize the bend and to ask the horse to transition upwards to the canter, without taking any pressure off the inside leg. The inside leg MUST remain consistent.
My old trainer also told me to lift the inside rein while maintaining consistent steady contact on the outside rein. What I found worked better for teaching my horse the lead though, was to pull back a bit on the inside rein instead of lifting up.
Second, rushing a horse into a canter will not help him balance up in any way, which is what it sounds like this horse needs to do at this point; rather, it just teaches him to rush through transitions and hollow himself out. What you really need to do is make sure he is very balanced and at a consistent pace at the trot, then sit and ask for the canter. If he breaks into a fast sloppy trot, slow him back down to a balanced trot again, reorganize yourself, and ask again, making sure your cues are very clear. To give him the benefit, ask on a circle or a corner; just make sure you are bent; it will help him pick up the correct lead.
Also, if he is stiff one way, do lots and lots of bending circles at the trot to warm him up before cantering. I like to do two circles in each corner; a big circle followed immediately by a smaller one. It helps a ton with balance and teaching them to engage the hindquarters.