Please don't use a german martingale for this. It will not fix the canter, and at the moment the last thing you need to worry about is where his head is. It will NOT get him off the forehand, any gadgets on the horse's head/neck will do nothing to get the horse off the forehand unless appropriate drive and energy is created in the hind end.
My new boy is a very green warmblood gelding, who has problems in canter. I spent 2 weeks lunging him before I even got on him as he was so unbalanced. I did not put side reins on him, just a bridle, saddle and ran the line through the bit and over his ears. Just to allow him to find his own balance without interference.
Under saddle, I have worked diligently in maintaining his relaxation, rhythm and balance in walk and trot, and ensuring that he has a very good 'go, stop and turn' button.
I did huge amounts of work in leg yield and shoulder in, in order for him to gain a stronger understanding of working into an outside rein contact and coming off the inside leg.
Multiple transitions - working on a 20m circle I would put in a transition every 1/4 circle, between gaits or within gaits.
Multiple changes of rein and working on 'snowman' figures, so going from a 20m circle, changing rein onto a 15m circle, changing rein onto a 10m circle and so on.
I did not canter my horse under saddle until he had been worked 5-6 days a week for 2 months doing balance and strengthening exercises under saddle and on the lunge.
You cannot force balance or speed it up. All you can do is work on it step by step, always keeping the horse confident and relaxed. If you feel that the horse is losing balance in trot, then bring him back to walk for a few strides before trotting again. Never allow him to work in the same gait at the same tempo for more than 20m at a time, as this is where the horse will start to come unbalanced and fall onto the forehand.
When I started asking for canter, I would ride a spiral in trot form a 20m circle down to a volte, spiral slowly back out and while still in leg yield, get off his back and ask for canter. It is important to get off his back in this early stage, as it allows him to find his balance and for his back to come up under you, without trying to deal with where your weight is.
Try to remain nice and quiet, be a passenger rather than a rider for a little while. Just let him canter on a nice wide 20m circle, give him a fairly long rein and just let him work it out for himself.
Don't make a big deal of canter, and don't set aside a whole ride just to work on it. Simply 'sprinkle' a few canters in here and there, when you feel that he will easily 'pop' into it from trot. These opportunities will gradually increase, and eventually you will be able to ask for canter whenever you wish.