Everything in China changes without notice. Hainan now DOES NOT issue work permits without a Z visa. I was told I was the last one to do that in 2012, and I was working for a public university. I suspect Hainan University has the 'guanxi' to still do whatever they want. But you can be sure that a private school cannot do it for you. If you are from the United States, for some time we have not been able to change visas in Hong Kong. Please check on that before you fly there. Other teachers from European countries have been able to change visas in Hong Kong, I'm told. The writer of The Middle Kingdom, an excellent site and a friend of mine, left Hainan several years ago.