Extending my stay in China between jobs

Hi I have been working in China at the same school for the last 8 years. However, I decided to change jobs for this year. The new job requires a criminal record check and a medical which a completed several weeks ago. They also required my degree to be authenticated. Now, I applied to have this done over a month ago and still they have not processed this. My working residents permit expires at the end of the month (28 feb) and my new school has told me that there is not enough time now to do a transfer of my visa. They said now they will have to apply for a new working Z type which will take 4-6 weeks. Can I extend my visa within China while this is sorted out or do I have to go to Hong Kong or back to the uk?
Thanks for your help