The real advantage that the private school have is they are located near bigger cities where club soccer is offered. Most players at private schools can afford to play club. The rural players can not afford the cost and the travel. I know some clubs offer scholarships to play but the travel is the big problem. Many rural players do not have transportation for all the practices and games. Therefore they do not play soccer year round and it shows during the high school season.
The private schools are only abiding by the rules that the high school league has approved. I think a rule change is needed so coaches can work with their whole team with the ball during the off season. Almost all the soccer players at the rural schools play other sports during the off season due the small number of available players. Allowing the coaches work with the team during the off season would help even the playing field.
I am sure the private schools would appreciate the better competition within their classifications. The athletic directors need to address this with the high school league. They are the only ones who can repair the problem and make high school soccer better. Talk to them.