One option is to get the parents of the kids involved and set up a 501c(3) booster club to handle all the bank accounts and fund raising. Then all you should need is someone at the school to help with the eligibility grade checks before tournaments. If you're unable to associate with the school, it will have to be a county club or something of that nature as opposed to a school club.
That’s pretty much his how we are set up. We are considered an “after school club” and have a teacher that does the grade checks. We met with the principal and got his approval before doing any of this. Set it up as a 501c(3) with our own bank account. The bank account and 501c(3) can come later as you get established. We had a parent with a business that helped set up the 501c(3) part.
If you want to stay fishing right now just get a teacher to do the grade checks and just do one step at a time.