> I think I recall hearing somewhere that the Nationalists hit the Japanese in Shanghai specifically to overextend them, but if someone can speak to that with more authority I would appreciate it.

By no means an expert, but I'm currently reading China's War with Japan 1937 to 1945, by Rana Mitter, and that's pretty much what the author said about the battle of Shanghai, it was an additional front to tie up the Japanese and show them that China was prepared to fight. This was important because the Japanese were already advancing rapidly in the north. Chang clearly put a lot of importance on the Shanghai front since he committed his best trained troops to it, and they took appalling loses.

What was most interesting for me to learn is that the Japanese, after the Marco Polo Bridge incident, were not expecting much resistance and thought it would be a repeat of when they seized Manchuria without a fight. That China resisted really baffled and surprised them. They didn't even formally declare war on China. In fact, as late as the fall of Nanjing, the war was still being referred to in Japanese circles as "The China Incident." Chinese resistance and the loses they were inflicting on Japan also caused rage and anger among Japanese troops, which was likely a factor that caused the Rape of Nanjing.