I'm going to offer a dissenting voice and say I don't think this the right way to go about this. We own the moral high ground against the objectively immoral trans stuff (teachers grooming kids, hormone therapy, 6'4" male athletes playing women's volleyball), but charging people with fraud and potential jail time for referring to themselves by the opposite pronoun is also stupid, and more importantly, will backfire in the court of public opinion.
One of the most important things with the current administration is not to overreach beyond what is just, because every time that happens, the political pendulum inevitably swings the other way. If the left hadn't gone so far over the last 4 years, Trump might not have gotten elected again. (Thank God they did.) The trans stuff has been artificially propped up by USAID and others. Just stop feeding it institutional money and attention and it will wither away.