This sounds a lot like my mare. I agree completely with Spastic and smrobs. I would like to add that I would completely throw the reins out. When she goes too fast, channel her in another direction (circles, serpentines etc.). I personally like to keep the feet moving instead of stopping. When they move out faster than I like I usually either circle or pull them into a rough roll back using just one rein. I avoid pulling on both reins as it encourages bracing and nosing out of the bridle. Also most horse's associate a loose rein with going faster.
You want to be asking for bend in the corners, and trying to keep him calm in between. He should be between you, not rushing or making the straight lines you want wiggly. It doesn't have to be perfect at this point, it just gives him something to do. Bending exercises generally keep your horses mind on the work and on you. You just want to channel his energy into performing a task instead of him just running around with you trying to haul on his mouth to slow him down.
Does she stop when you sit down in your seat? If she does, try and channel this. Try and sit deeper in your seat, relax and slow your body down. Don't ask for a stop, but almost. If she wants to stop, squeeze her on so she keeps walking forward. You could do this when working on the serpentines. In the middle, you could ask her to one rein stop, bend to you, disengage her hindquarters, then go foraward.
Another thing you could do would be to be walking down the rail, then bring her to stop at a 45 degree angle to the wall. Have her stop, back up a few steps and pivot so she is facing the opposite direction, then walk off. This should get her using her hind end.
Here are some more exercises you can try. They are taken from 101 Dressage Exercises which is a great book if you can get your hands on it:
Shoulder in. Walk down --> do a nice round counter clockwise 10m circle in the corner and get back on the wall. While you are walking up the wall, ask for shoulder in for a few paces, walk off. My barrel horse likes this and gets him moving off my leg.