Interesting topic. I've actually been offered a job in Huludao next semister to teach english. I won't mention any names of the school, for the sake of being civil, and for privacy reasons. However, it seems that most laws in china are bent with a little extra money. I've been told that i can work with a business visa (F-visa), but it's only good for 8 months.
I've heard a lot of people say it's for short term business trips. Which the Embasy's website says so also. I'm just curious what the fuss is all about. If it's for business purposes, and the school writes you the invitation letter, it would seem legal, at least for the duration of the visa's validity.
From what i've noticed though, most schools can get a z visa, but you can only get it if you have a bachelors degree or higher.