You'll need a fake degree to get that Z visa- maybe the school will help you out with that. You are going to have to trust to the experience of the agency Maybe they will know a school which can keep on extending your 'F' Visa.. Either way if you really want to do this, really want to teach in China, you can't afford to listen to old fuddy-duddies on this site who tell you it's just not cricket. They don't play cricket in China and illegal working is considered respectable by most Chinese. Suggest you do a correspondence degree when in China. Good luck. Please tell us how you get along.

Taffy's post, see above, deserves deletion in my opinion!