I am fairly sure that American airlines no longer allows stopovers on award tickets. One thing you might want to consider is that Korean Airlines flies direct from LA to Sao Paulo and you can use Chase points on Korean Airlines. Korean may also fly from San Francisco and/or to other places in Brazil. I've just never had any reason to check. But it's an option that not many people consider. I did the L.A. to Sao Paulo trip and it was much better than most airlines.

Check out a website called Award Nexus. You may be able to do some free award searches there. If you have to pay, the cost is reasonable.

If you are headed to Rio, your biggest problem may be finding a hotel during Carnaval.