If the horse has no teeth problems but is still having trouble with the bit (which is where your bridle problems are coming from), his current bit may be uncomfortable for him, or bits in general are uncomfortable for him. You might want to try bitless. Try riding him in a halter with reins attached and see how he goes, a couple years ago I did this on my mare and found her so much less combative that I went back to the english mechanical hackamore she was started in. If you're doing gymkhana or pony club or jumping classes, it shouldn't matter whether you have a bit or not. Dressage, and other disciplines, they want bits, but for what you are doing you could go bitless. He would probably be much happier, but you won't know until you try!
The reason I say bitless is because in the picture from the other thread he looks uncomfortable, and you say you have a bridle issue even though his teeth are fine.
"You can do something wrong for thirty years and call yourself experienced, you can do something right for a week and experience more than someone who spent thirty years doing the wrong thing." ~WhattaTroublemaker