

Q2 visa to tourist L type
I am currently at the end of my Q2 type, with just a few days left. I want to stay one more month in Beijing, but I am missing one document in my application: my (Chinese) grandmother's hukou. When I applied for the same Q2 in my home country of Australia, I only needed her shenfenzhen Chinese ID card and a letter of invitation, plus all the usual passport requirements. I tried to renew it in Beijing but they have extra requirements here including proof of relations (found all the birth certificates), house deed (got it) and the hukou (grandma has lost it...) So I'm in a predicament.
I'm thinking of two options. Either go to Hong Kong just before it expires and apply for a new Q2 type (is that possible?) with the documents I have. OR try to apply for a tourist L type in Beijing, without traveling out of 'mainland China'.
Hoping to hear any suggestions - time is of the essence!! Will have to exit on Sunday