Thank you for your help. I also found the visa page on the Chinese Embassy site in the US:

http://www.china-embassy.org/eng/visas/zgqz/t943855.htm

#4.1 seems to address the situation and does not refer to leaving any of the cities - just applying to stay in the city. I am unsure if we will have time to do so anyhow after looking at things to do in Shanghai. I may just email the embassy directly and ask. If I do I will post the reply here.