Since the new head English teacher JANE took over the position.....

Yep, this can be a problem, even in the state sector! Somebody like her is the worst kind of boss you can have. Chinese women can be ruthless in positi ons of power like hers. She will get ahead in two ways simultaneously, by being a crawler to the leaders while denigrating those she is in charge of.
This has also happened at a county senior middle school supplied with foreign teachers by a local Chinese company/recruiter. Said state school had 6 foreign teachers dismissed last winter. This past term the first one lasted just 2 weeks. I lasted until the end of the term. My teaching assistant, the longest server as such in the company, was fed up with our 'Jane' too. Though the school only employs one foreign teacher, and 'our Jane' was never impolite to me, I know only too well she can be a backstabber from her past actions. Every week she attended my lesson, and pointed out my and my teaching assistant's shortcomings at its conclusion. That's unusual in China at state schools. Before her appointment, foreign teachers were never dismissed. But if one wanted to bring her reign to an end, that would be nigh impossible. Anyways, I got paid in full, and am not required there this coming term. That's good. My company offered me a new contract and has posted me to another senior middle school. Even better!
When we are in bad situations, we should do our best to last out until the end of a term or the end of the contract. Then we should get out of there and find a new school. Chinese bosses can make your life a misery - either that boss, as the head English teacher of your grade, or the school FAO. Before accepting a job, bad vibes from either or both should be a red flag. It wasn't in my case because I needed a job fast at that time - it was Hobson's choice for me!