In every proceeding or action brought under this article, the court shall rule whether the anonymity of any woman upon whom an abortion is performed or attempted shall be preserved from public disclosure if she does not give her consent to such a disclosure. The court, upon motion of any person or upon its own motion, shall make such a ruling and, upon determining that her anonymity be preserved, shall issue orders to the parties, witnesses, and counsel, and shall direct the sealing of the record and exclusion of individuals from courtrooms or hearing rooms to the extent necessary to safeguard her identity from public disclosure. Each order under this section must be accompanied by specific written findings explaining why the anonymity of the woman should be preserved from public disclosure, why the order is essential to that end, how the order is narrowly tailored to serve that interest, and why no reasonable, less restrictive alternative exists. This section may not be construed to conceal the identity of the plaintiff or of the prosecutrix or of witnesses from the defendant or to abridge or deny the defendant’s ability to conduct discovery under applicable rules of court or the defendant’s right to a trial by jury or to cross examination.