How can I work with administrators who lack expertise in my field but evaluate my work?

As it happens, both my current principal and vice principal came through these programs

That is the biggest tangible problem. And the root cause of the situation is why they were chosen, and who chose them. You do not deal with a localized problem (a nice person suddenly turned bully), but with something else.

You do not have many attractive possibilities.

1. The safest. Just do what you are told. Fsck the teaching of things to others.
2. The rebel. Continue being a teacher as you did until now. What will happen will happen. You will probably not like it.
3. The revolutionary. Contact the authority overseeing your school, and complain. They might actually listen to you. Or they will not undo their decision about sending your supervisors to you. It's a gamble.
4. The guerilla fighter. See if the students and their parents are on your side. If yes, ask them to take the fight on their hands. Many can do more than only one. I do not know what will happen if your supervisors (or their superiors) catch wind of this.
5. Quit, find another job. Maybe as a teacher, maybe as something else.