Thank you to everyone for your advice. The morning of the race I spoke to one of the executive directors of the league, who said the rule was in place to protect the school, not the league, so he would not punish us. I understand that it would not necessarily justify having them compete, but the head coach said he did not want to prohibit a kid from running on what was a coaching mistake. Later, the vice director told me simply to start accepting the proper forms from now on.
After that competition, I decided to try to standardize the forms. I quickly found myself in a Catch-22 when I realized that the required form (posted on our league web page) was copyrighted. I do not believe the league has the permission to post the form, because after some calling around, I had to pay about $25 - $30 to order fifty forms from one of the copyright holders. I doubt that many people even know about the rule to have a standard form (our Athletic Director did not) or that the form is copyrighted. I am trying hard, but please pray for me to act appropriately as I try to sort this out.