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on a trampoline, it always helps me if i kinda set up the spin with my arms in the air of the jump before i spin. when in the air, i always try to look over my shoulder, and it for some reason it really helps me to spin faster and more in control if i sorta tuck my legs up. but it may be different for you.
i cant really help to much with a diving board though, because i have the same problem. the bounce from the board always throws me really weird.