Six day transit through Beijing to US

Hi,
I am a holder of a US passport currently in Australia on a valid visa, and will be flying through Beijing on my way home to the US. I will be staying in Beijing for only six days, but I will be staying with family there. I booked my flights separately from Sydney to Beijing, and Beijing to NYC. Is it possible to just get a G type since I will only have a six day stay and I am in transit to a third country? Or do I need to apply for a L type because I will be staying with family? Thanks!