ETR hits on a key point here. Network your butt off. <!!WTF!! Did I just use a slang, buzzword noun as a verb? Wonders never cease!>
First, your connections among other foreigners are often connections to other local jobs that need (or will need) filling. Second, your connections to Chinese teachers and even at your present private can also become leads to public schools that have a steady, long term need for foreigners.
ETR's closing point is pretty obvious, but bears repeating. Decide what you want, and put your plan into gear as early as possible. No, you can't rush the decision makers, but you can get your name out there.