Perhaps this well help you.
The competition for scholarships is not between you and the other 300 players who are trying to get one. Most of those kids have no chance.. so you're only competing against a very small group of really good players. You're chances of securing a scholarship are much better than you realize, assuming you are a one of the really good players.
The schools are looking for great players, the great players are looking for schools.. Let them know you are out there and if you are good enough you will get a scholarship.
The vast majority of players will not get a scholarship because they are not good enough. The majority of players who are good enough will get a scholarship if they make enough noise.