Lose the tie down. Its design is not meant to keep a horse's head down.
I myself do not like twisted wire in any bit, IMO. I would put her in a smooth mouth snaffle.
No bit you put into her mouth is going to change what she has been TRAINED and allowed to do up until you have gotten her. It is going to take months to re-train her to understand that she doesn't have to go-go-go-go all the time.
As BlueSpark said, do tons of circles and tons of serpentines. You don't want to have constant contact on her mouth with both reins all the time to slow her down; that's what makes a hard mouth. Instead, use a direct rein (one rein at a time) to do circles and serpentines.
Let's say you are walking along on a loose rein. She breaks into a trot. Let her go 2 or 3 strides (so it sets in), and then ask her to circle in a small circle until she has to break down to a walk. Then let her walk on. When she breaks into a trot again, ask her to circle back to a walk. Repeat, repeat!! You can mix up which circle direction. This will take a looooooong time for her to get the idea. I had very similar problems with my horse Red last year where he just wants to go-go-go. We went for a 2 hour ride one day and I didn't get any farther than 1/2 mile from the barn .... because he'd break into a trot, and I'd circle him. He didn't catch on very quickly that going faster meant circling.
Eventually, you'll get to the point where she'll quit trying to rush the walk.
Then you can repeat the same exercise at the trot. If she breaks into a canter, circle.
Always remember to RELEASE rein pressure when she gives.
If she throws her nose when you apply rein pressure, do not give until she gives to you. Do not pull with both reins; that sets you up for a rear. Instead, I like to (for example) take my left direct rein, and twist my wrist up and toward my right shoulder. When the horse GIVES their nose nicely to the rein, then they get release. But if they pull, I hold steady until they give.
And you must be consistent. If you let her throw her head without punishment (giving to the rein) or if you let her go into a trot without you asking her to, you have just set yourself back in training. ALWAYS correct her. ALWAYS be consistent.
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It is not enough to know how to ride; one must know how to fall.