Once you're talking about legal work in China/Z visa, you can work only at Z sponsor, which must be authorized for foreign hire by SAFEA, in order to get Working permit and Invitation letter, both documents needed at Z visa application.

There are Co's. in China, who hold foreign hire authorization, and have Contracts with schools around China, where they send FTs once they arrived to China with Z.

You might get more info on such possibilities from Visa agents.

Here's one:

http://www.fbt-chinavisa.com.hk

Accept illegal work, accept the consequences.

Let's look at your question. Is there a legal way to break the law? No. There are ways around the law, but I'm not going to make myself an accessory. 

just take the job on a student visa dude. no one will care.u r just teaching kids, not like working for NASA. 

If any one asks , your just a student there. Although keep in mind if ur gonna work illegally forget about ur rights. So either u suck it up and take a risk or let it pass.

its better you dont do it in the illegal way. student visa is easier to get but you have to renew and pay a lot for that. as you can have a treaty trader visa why hustle contact with a legal firm in shenzhen or gz hi touch is a good legal farm you can consult with them 

its better you dont do it in the illegal way. student visa is easier to get but you have to renew and pay a lot for that. as you can have a treaty trader visa why hustle contact with a legal firm in shenzhen or gz hi touch is a good legal farm you can consult with them