If you are still having trouble when you go back to a bit(hopefully a snaffle), try this method. It is a method I learned from watching Clinton Anderson shows and DVD's. It may take some time, and will not happen overnight(there is no miracle cure for anything horse related) You want him to learn to be on the bit, to give to it. Changing up to a different bit, even for a short time, will not cure the problem. You must go back to the basics. I saw that someone mentioned lateral flexing. That is exactly what you need to do, but you have to do it right. The key is giving him an instant reward(dropping the rein) the split second he gives to the bit. So you will reach down the rein as far as you can, pick up one rein, pull your hand back to your hip to bend his head around. Hold it until he gives even the slightest slack in the rein(it doesnt matter if he doesnt bend his head much), the instant he gives any hint of trying to give you slack, you drop the rein like it was on fire. You can start this on the ground if you prefer, if he is really hard mouthed he may fight quite a bit until you get his first give. You must not drop the rein until he gives. If you do this and immediately reward him by dropping the rein, he will be bending his nose to his belly in no time with just a light touch on the rein. Do this until he is light on both sides. From there you can progress to verticle flexing. Do not attempt vertical flexing until he has lateral flexing down. This is done the same way. Pick up on both reins and pull back with equal pressure. Do not release until he drops his nose in even the slightest bit, then drop both reins to give him his instant reward, or at least let them loose if you do not feel comfortable dropping them. If you follow this properly, you will probably never see him push his nose out on you again. He will be on the bit for good. I have used this method on several horses, including one like yours that was hard mouthed, and it has worked perfectly.
Hope this helps. It is pretty simple and it works wonders. Clinton Anderson's methods are for us average owners that aren't experts, and never will be experts, but helps us safely help our horses be better.
Good luck, and I hope you decide not to change to a stronger bit.