L- visa extension in china

First, you may need to provide your passport, the completed application form, a recently-taken bareheaded color photo, registration form of temporary residence, accommodation arrangement and the return ticket. Then, submit the application to the exit and entry administration of the local PSB within China.

what reason can i give for wanting a long extension of 6 months?

You can explain your situation and state that you do need 6 months to stay in China. The consular officers will give you proper stay of duration based on your situation.