How can I bypass the teacher application process to avoid HR?

I love teaching. I've been a classroom teacher for several years. My last position ended with a layoff, I've applied to dozens of posted vacancies, and I wait and wait and then get a standard rejection message. I've had a few interviews, indicative of my materials and process working, but they don't go anywhere.

So, I'm wondering if there's a way to bypass HR whicj presumably receives every incoming application on SchoolSpring or whatever ATS platform they use.

I've sporadically emailed principals and department heads after submitting my application. If I get a reply, it's to wait for the system.

What else can I do to get back into the classroom?

People say there is a teacher shortage. I don't see one.