In some states, if you are not picked by your school or your local chapter, you can contact the state direct and if you are willing to pay your own way or find your own sponsors, they sometimes have extra slots available. My son paid his own way(not picked by high school), My daughter (Home schooled) talked a local bank and an attorney into sponsoring her. Our state was about $350. my guess is some might be a good bit higher.
Really ticked his high school off by the way, Guidance counselors thought they CONTROLLED the process. So go direct to state don't believe everything you are told. Again probably every state is a bit different.