Temporary resident permit in Wuhan

I am an U.S passport holder, and my parents are Chinese. I am going back to visit my mother in Wuhan this year, and I tended on applying for a Q visa, in fact, I submitted all the necessary documents for a Q type. But the visa agency sent me back a tourist one that is valid for a year with multiple entries for durations of 60 days.

My flight itinerary is from June 10-August 11. I leave on the morning of August 11, the duration is roughly 61 days. Should I apply for a temporary permit from the local Public Security Bureau (PSB) Exit and Entry Administration office? If so, where is that location in Wuhan?
Or would they overlook the overstay of 1 day?
Any advice would be greatly appreciated!