I am living in Shenzhen and I need to get a z visa so I can do my job as an English teacher.

Scott, you can apply on your own or assign an agency to help with your application from the CVASC branch in your area. There is no agency recommended by the CVASC. You need to find one on your own. In fact, it isn't as difficult as you thought. With the help of your employer, you still can apply the Z type.