My left eye turns (severely), has since birth. I had several operations in infancy to correct it, and they all failed.
My eye still turns out, and no amount of patching or exercises has ever changed that. You can temporarily control it, but my eyes do not work together. I have little grasp on depth perception - the only thing this effected was my tennis game and joining the air force. The exercises do have a measurable impact on my actual script though. (Also assuming you have discussed prisms in his glasses with the optometrist?)
I do get funny looks, and a lot of grief at school, but in the end, it honestly has no real impact on my life. I have other issues with my eyes, so I have worn glasses literally all my life.
Keep persisting with the patching, the exercises, but don't let it become a bigger deal (aesthetically speaking) than it actually is. The only time I am ever self-conscious of it, is when people keep going on about it and trying to 'fix' me.

Just a perspective from the other side. Good luck.