I like the sugunda bit!! Sometimes a stronger bit isn't the right thing though maybe just try to soften your hands(take and give) and your seat/legs but lean back and sit deep into saddle!! Try and use your other aids and your flat work more in between jumps and before and after jumps!!:) Without good flat work it'll be harder to jump and won't look as good!!😊
Ponies + Kimberwick = a tad more control. If the reaction to the bit is a bit more respect it means you don't need more control hence softer hands. This also means that you must learn to feel for that moment the horse yields to you and your instant reaction must be to soften the contact. This is actually the only way to teach a horse to respect contact-if you respect the horses mouth.
I personally do not think that a new bit because a forward horse will just run through another bit given enough time. I think what might help is to ride more from your core and use different aids to keep control.
maybe a elevator with a single rain in the middle. but always remember that the bit is only as soft or harsh as the person using it. so if you have nice soft hands than most (not all) should not "hurt" the horses or pony mouth.