You’ll not be able to get an extension to your Z visa (technically your residence permit) without actually having a sponsoring company do all the work for you in China. Multiple-entry F visas are getting harder to get in HK and tend to be for those with HK ID cards - the 6-month ones anyway. I’ve not heard of anyone getting a 12-month ME F visa recently, even HK residents. If you’re Australian, you might be able to get an APAC travel card if you have the requisite contacts in OZ to process one. That would allow you 30 days at a time.
On the F-visa situation. Satellite TV says there are many foreigners working illegally in China on F visas. However, I would like to point out that people setting up companies in China, and those sent over to supervise sub-contractors or suppliers have no means of obtaining work permits and Z visas because there is no entity to employ them. In the first example, the employing companu has not yet been set up, and in the second, they are not employees of their suppliers, but their employer abroad does not have a local PRC entity which can employ them. I would not count these people as “working illegally”.
I would agree though that part of the difficulty in getting F visas now is the large number of people in Shanghai and Beijing just “hanging around” on F visas and working. This is more a tax issue than a visa issue as of course these bods don’t pay China’s crippling rates of income tax. That’s more likely to be the government’s thinking when wanting rid of them. I don’t think previous F visas are going to preclude anyone from getting a new one if they fit the criteria, but I do know that those who get them by paying travel agents in Hong Kong to bribe officials in border stations at She Kou and Shen Zhen are having difficulty, and F visas issued inside China are now frowned upon. My missus has an L (tourist) visa issued in London and it can be extended for up to 6 months. Now this is single-entry and cost £145, but they also do multiple entry F visas in London, but they are extremely pricey (over £200). If you have the proper docs, they will also do 12-month visas. In this case, and if your company is paying, a trip back to your home country to get a year’s F visa might be an idea, especially if it coincides with a family reunion visit.
Simply stated, the PRC has gone off HK quickie issued-inside-China visas and prefers you go home to get one. If you do, then from my experience there’ll be no problems. Similarly, if you apply direct to CTS in HK with all the correct paperwork, there should be no problem. This would probably be the case for a Taiwan application as the visa will be issued by the Misnitry of Foreign Affairs (i.e abroad) and not the Zhu Hai or Shen Zhen border police. [The point was, visas issued inside China could be valid for a stay of 6 months, whereas MOFA visas were only for 30 days at a time over a 6-month period. So, useless for actually living in China on, but good enough for legitimate short business trips.]