Right now there is an anti-incentive to spread this contest around as it directly goes against the chance of winning.

I Run a contest myself and as a way to promote it I've put aside part of the prize pool for people who resteemed. Put 20% or more of the prize pool aside that gets split between those who resteemed and predicted the correct US Open winner. This way many people can win something and there is a good reason to participate and spread this around like crazy at the same time without any obligations.

You could make an announcement post with the rules of the contest and have it spread around. Once the quarter finalists are know you could make the actual contest post with the start of these matches as a deadline.