To leave before your contract is up would not be wise. You'd probably miss out on at least two weeks' salary, not to mention travel allowance money for the Spring Festival holiday and/or air fare reimbursement (or part payment). Furthermore, you'd have great difficulty getting through airport customs if you decide to exit the country early without sorting out your Z visa first, as your residence permit would still be in date.
My advice, first fix up a new job. Then 'negotiate' terminating your present contract by mutual agreement.That would be the sticky part as you'll probably lose some of the money they owe you.
But of course, you can always do something as a last resort that will lead to you being fired - an extreme course of action indeed!
It all depends if you can get fixed up elsewhere, preferably in the warmer South, difficult right now as it's well into the 1st semester. But there are some ads for 'winter camp' teaching.That would tie you over until the new semester begins, provided you can get a new residence permit and another new job before then.
I don't envy your plight. You have my sympathy. Good luck.
Unfortunately it's too easy to get hired by ropey schools and colleges - there are loads of them here in China.