I personally really like Pelham bits and they work really well with a lot of horses, or a gag bit if the horse needs more lifting up since Pelham kinda tries to bring the neck down. Or if you need just a bit more effect I would try a double noseband! According to my experience it adds a little more power to the bit.
My stable uses elevator bits quite often cause all of our higher level jumpers are certainly handfuls. If you ride on the bottom ring I would use double reins. There's also a Pelham and that's used frequently in the show jumping world at top level