Rider needs to sit back and needs more go for some of these jumps. Also, her hands are not as quiet as they could be. The head tossing before/after the jump needs to be addressed also. Especially in hunters, this will not be very favorable in the show ring. Have you tried a martingale with her?
When training OTTBs that rush after the jump, my trainer always has me halt right after going over the jump. Sometimes it's ugly, but it works very well for stopping the rushyness. You can also try going over entirely in trot. Come up to the jump in trot and leave it in trot. I know for the showring, you need to canter out of the jump, but while schooling, getting her to trot out of it may be helpful with the rusheyness. With both of these techniques, you need to try it quite a few times before seeing results, which means lots of schooling.
People always forget that a jumping course also contains flatwork, so when schooling for the show, it can't all be about jumping. Looks to me like this rider and horse need to go back and do more flatwork to get a good, balanced, corrected canter going consistently before heading over jumps.