Been there done that is indeed correct as to the current visa situation. 4 or 5 years back it was still possible in some areas to get an L converted to a Z. There also might be a few isolated areas where local officials will still do this. You have to understand that China is not as homogeneous in their laws, or their application, as other more developed countries are. That said you won't find too many places where such a conversion is possible. The olympics did not help either, as during that time regulations were tightened up quite a bit, and were never fully returned to their prior state afterward. Now it's near impossible to get an L converted "within" China, though you can still have it done in HK. However, that isn't even always true, and in many cases people are being required to return to their home country. It's kind of foolish really, the China are shooting themselves in the foot, as they are making it more difficult for foreigners to come and work here. We pump a lot of money into their economy, so it seems foolish to me to make it more difficult to come here.

At the very least you will have to go to HK to get a Z visa if you are already in China, and don't expect the school to pay for your trip there, or for the cost of the visa, or for your stay in HK itself. Schools more and more are showing a preference for only hiring people who are already "inside" China, that way they avoid having to put out any money at all. You end up flipping the bill for almost everything, while if they provide a Z visa before you arrive, they have to pay for a lot more.

The advice that you should not come here without first having that proper visa still stands, but it is also becoming less and less common for schools to "want" people who are outside of China, so as to save money and hassle. After all, if you are already here they can not only save money, but they can get a sneak peak at what you can and can not do as a teacher before they even fully commit to hiring you.