I flew a DH to PVG connecting to another DH to the US last summer. The only issue is that they don't do a transit connection where you can check your bags through to your final destination. You must clear immigration and customs, claim your bag the same way you would if PVG was your final stop. Then you have to re-check in with AA (in your case) as you would if PVG was your starting point. So, save yourself some time when you plan your connection there. Also, let the immigration officer know you are a transit passenger.

I'd second the recommendation to try the Cathay option. Even if you can only afford business class, it's still head and shoulders above the AA first class (especially if it's the newest version of their BC product - highly likely on a US route).