Z status visa about to expire - new job - current company won't transfer or let me leave earlier

The current employer won't transfer my stuff. I don't know what to call it. I know that I have a Z status and a residence permit. They both expire on the same day as my last day of work. My current employer will not let me end employment sooner. If I could then I would have been able to submit my documentation for a transfer. Now because it will expire than I will have to allow them to cancel my current residence permit. So what they will do is support and get me an H visa which is good for 30 days. During that time I will then be able to start the process of giving my release letter from old employer to new employer. New employer can start process to obtain new Z type or not? I will also need to get a foreign expert certificate but I'm not sure if I can get one before the H runs out? I'm so confused. I need to basically get a new Z type which takes while in china how long? I'm American. Then apply for the expert certificate but how long does that take? Am I going to have to leave for Hong Kong? Someone told me that but why? Why can't I do something now instead? Is there anything I can do? Would getting my release letter earlier change anything?