It would help if you would specify the province you're in. I suspect that your province abides by the national guidelines issued by the foreign affairs office based in Beijing regarding the issuance of Z visas to foreign teachers. However, it's a fact that there are foreigners from your part of the world teaching with Z visas and appropriate resident permits in certain Chinese provinces and autonomous regions, those that choose not to follow said guidelines. Though such foreign teachers will have a local foreign expert certificate, it can't be transferred to another province. Without a foreign expert certificate, a z visa can't be issued.

However, there are foreign teachers with Z visas working in other provinces that won't issue them with foreign expert certificates. But the accompanying resident permit is not for the area where those foreign teachers are working. It can be done in this way where you're based.