don't do a harsher mouthpiece, especially not a slow twist! (It is severe despite what people may think) The key is more flat work, more training, more practicing, perfect her speed over a course small in height, etc. If you must bit up, use leverage rather than a harsh mouth piece. I would keep the mouth piece soft as possible, such as a lozenge, but use a pelham or elevator. If you do, please, please, please use a curb chain! Many people use one on a Pelham but not an elevator, an elevator is a leverage bit and therefore requires a curb chain so it won't over rotate.
I would highly suggest using leverage instead of getting a harsher mouth piece. Since you're doing lower level eventing, using double reins shouldn't really be an issue, and if you're only going to use one rein, please use a bit connector. I prefer using two reins because you can use the bit as a regular snaffle and then use the leverage only when needed, but with a harsher mouthpiece, the horse is forced to deal with the increased pressure/pain without relief. I would try an elevator bit or Pelham and go from there. You could even try finding a leverage bit with the same mouthpiece as you have now to see if that would work.