I've wondered about this for years. To my understanding of the rules, a long jump is measured from the take off point to wherever the sand is disturbed closest to the take off point. So, if it doesn't matter which body part disturbs the sand, it shouldn't matter how you jump. Just wondering if a forward leap with a hands first landing (dive and roll) might take you farther.
I suppose you could test it in a pool. Beep, let us know.