This horse needs to go back to the basics, and right away--she shouldn't be jumping at all, at this point.
Unless the horse is in pain because of the tack, you cannot use that as an excuse. She is resisting the entire time--that is a lack of training, not a cry for a magical change of bit. No matter what you put on her, she will rush and ultimately, ignore your commands, which is what she did heading towards the jump. You /can not/ ride a excitable horse in a stiff manner--they pull because there is something to pull on (your stiff hands). This then becomes a habit, because the horse balances herself on your hands.
Bottom line is, you cannot hold a horse back with a bit. It doesn't look nice, the horse resists the entire time, and you become a stiff rider. If you always ride her with a stiff back and arms... where is her incentive to change? The horse doesn't think, 'well if I just calm down, she'll relax too'. You need to take her back to flat work, working on lateral work at the walk and her giving her face without any training aids. You cannot move up into the trot until she does this calmly. Even excitable horses can move in a controlled manner; because as she is now, she is not a pleasure to watch--say goodbye to any equitation classes.
I just cannot stress this point enough--you cannot hold a horse back the entire time you ride--she must learn to go the speed that you request and stay there until you say otherwise. If she can not handle that... you shouldn't be jumping her.
Someone told me this once about bending, and it applies to all forms of riding--if you want your horse to be soft and supple around your leg, you can't have it be stiff as a pole--what horse will want to bend around that? In order to have a horse be soft, YOU have to be soft, too, and all of the time. That's what a trainer does--shows the horse what is correct.
With that being said, I know it is hard to work with someone else's horse when you cannot make changes... if anything, this horse needs to be put in a softer snaffle to learn the basics. But no bit is too harsh, only hands are. I believe the horse can go far, if you bring her back to the simple basics and get her mind on your and your aids... not other horses or jumps.