Here's Shiva Nata-- a sort of yoga that involves combinatoric movements. It would be easier to structure as competition-- the scoring could be based on the complexity of movement that a person could do accurately.

I think that goal misses the point. From the article you linked:

Continuous spiral movements consist of two complete counter-directional sine curves. Therefore, performing such movements sets a series of alternating active and passive fragments of the energy flow. These energy impulses purify energy channels and balance the circulation of energy inside them.

Synchronizing spiral movements of the limbs with the breath creates a constant and intensive energy consumption from the surrounding space, translation of it through psychic-energy structure channels, and accumulation and radiation into the surrounding space.

Complexity isn't the point but energy flow is. Those semantics are off-putting to rationalists. If you on the other hand simply drop the main part of the practice you are doing something like cargo culting. It might superficially look the same but you lose the essence.

I rather prefer to have bodywork that's from the ground up based on a more modern framework.

I don't think having competitions is necessary. But it might make sense to look at Tai Chi competitions. They don't do their Tai Chi patterns and see who does them the most beautiful way but they do push hands competitions.