Regardless, the rider should not need to rely on the martingale to stop a horse. I have a half saddlebred who's head can go straight up, especially when she's excited, and I never use a martingale, unless I really feel like it. You need to learn to stop a horse that has his head up. If the problem is that he's avoided contact by throwing up his head, follow your hands up to keep the contact with his mouth. Use one rein to turn him sharply and stop him. Also, are you asking for spots and he's just ignoring, or are you letting him just pack you around o/f?
As for getting strong, try transitions. Walk, trot, stop, trot, stop, walk, trot, etc When my mare got strong after interschool (because some kid hung on her mouth..) I did transition work, lots of backing up, and circle work. Does he ever get strong before the jump or when jumping, or is the problem just when you're hacking?
“Have fun - Stay on top.”
"There's nothing like sixteen hands between your legs"