I personally recommend a pelham with double reins instead of rein converter. Pelham are totally accepted in the hunter and infact, the classic hunter bit. The snaffle(top will give you light feel of her mouth and steering for when she is going well and the curb rein( bottom) would allow you to check her back every so often so she doesnt get too strong around the course.
Good on you for checking your mare out- I'm sorry if that came across as snotty, but a lot of people don't think of it. Yes, a slow twist is a fairly strong bit. If you've ever used double reins before, a Pelham might be something to try as well. A shanked jumping hack could also eliminate her ability to grab it, but would be quite strong.
I am currently taking dressage lessons, and my horse seems to love it and respond well. We have had her teeth done, new saddle that fits, and we've also gotten her chiropracted. So would you say a slow twist d-ring is stronger than the kimberwhicke? I have already tired the kimberwhicke and she just hates the leverage om it and that it has a curb chain. She also takes the bit and runs sometimes and that's when she gets out of control.
There's several different types of leverage- pressure on the bars and tongue, pressure on the nose, pressure on the poll, etc. A hackamore exerts pressure on the nose, and most bits exert most of their pressure on the tongue and bars. A kimberwick allows you to use more poll pressure with the reins lower. I assume you've had her teeth and back and saddle fit checked out to make sure she's not in pain before you start bitting up? You could try a slow twist, but that is a lot of bit for a horse that's used to going in a smooth snaffle. Also, if you're not already working with a trainer, I'd recommend starting to take lessons to soften up your horse and get her more responsive to your aids. Even if you never intend to compete, dressage lessons can help a lot when it comes to that kind of stuff.
You could give a kimberwicke a try- there's several different types of leverage and mouthpieces you can play with within that subsection of bits. I would start with a single jointed one with the reins on the middle slot for a three-hole or lowest slot for a two-hole. With a three hole, you can always move the reins down one more slot for more leverage- also practice stopping with your seat and teaching your horse to stop from a voice cue! A stronger bit is a temporary band-aid, not a permanent fix. Training is a permanent fix.