I have a friend I can stay with here, and will just leave after I get my airfare and final pay come the middle of next month.

As China needs professional foreign teachers like you, I hope you won't let the negative aspects of your employment at your present school sour you. I think you just drew the short straw that time. Stay awhile longer and do another gig lasting for the next academic year.
And thanks for posting about your recent experiences with that devious FAO. Sometimes what an FAO does defies all logic. Useful stuff for newbies indeed.