Disclaimer - I am not a horse trainer. The following advice is worth what you paid for it - nothing. Never do anything that you are not comfortable with or could compromise your safety. That said...
It sounds like you are unable to effectively stop or slow down the horse when he gets like that. So breaking down to a trot or slow canter will not work for you.
Assuming you have a safe place to do so, I suggest letting the horse run. When he starts to slow down, make him run faster. When he gets tired of that, make him run more. Do this frequently. He should get the point pretty quickly. After the horse is past ready to slow down, them slow him down. Speed control should always be your decision. When you ask for a gait (any gait) and speed, the horse should stay at that gait/speed until asked for something different.
You can do this at other gaits and speeds to reinforce the point.
The "won't stand still" is probably an easier thing to address.Practice standing still. You have to make absolutely sure you are not giving the horse any type of cue to move. You cannot fidget and expect the horse to stay still. As soon as the horse starts to move (his feet) start moving him as if it were your idea. Do tight circles, working trot, serpentines, hips over... the point is to make the horse work. How long you have to keep this up depends on your horse. Some are more stubborn that others. After that, stop again. Relax yourself. Rest the reins. Don't move your hands. Keep you legs relaxed and still. It is harder than it sounds. Most people I know with horses that can't stand still are ridden by people who can't remain still. Do this "keep still" exercise for 15-20 minutes each day.
As far as the bit... I don't see a problem with _trying_ a different bit (as opposed to changing to a different bit). Your current bit may be part of the problem. Your hands, or other cues, may be part of the problem. When I first started riding, people noted that horses usually went faster when I rode them. It was true - I was inadvertently cueing them to do so.
Don't be so quick to say "not me." Have a third party observe you and determine that. We all have bad habits that we are unable to see.
Be careful if trying a new bit. You need "softer" hands when using a "stronger" bit. I agree that it is the training and not the bit. But sometimes, a different bit can get the horses attention. Once you get the desired reaction, you can try going back to your old bit. If using a "stronger" or even different bit, the horse will very likely react differently. That may be a negative reaction if the horse doesn't agree with the bit or you pull too hard on a "stronger" bit.
For example, let's say you take a horse that has only known a snaffle or hackamore and drop a curb bit in his mouth. The horse could possibly react poorly if he doesn't like the bit. This problem could be magnified if you are using the same amount of pressure, since that pressure is now magnified by the leverage of the bit. Definitely not something you want to test on a running horse with no brakes.
Best route would be to get a trainer involved. He/she could evaluate the situation, see if you are contributing to the problem and suggest some solutions tailored to you and your horse.
Last edited by Tazmanian Devil; 01-23-2013 at 10:43 AM.