Can I apply for a work residency visa while within China on a tourist type, not z type?

Your never allowed to work on a tourist type (L) but a lot of people do and you probably wont get caught, however they will tell you once they have the work permit to apply for your work type (z) in Hong Kong. Applying for a Z type in Hong Kong can be done but it's not a sure fire thing, it depends on the schools contacts and relationships. Perhaps something to think about is putting a clause in yur contract with the school which states if you are unable to get a work type from Hong Kong then they are liable for a flight ticket home for you. Just an idea.