I have done this in GRU... Perhaps you can connect through there.
I haven't kept up with the current situation in GRU and CGH, however for what its worth. Some years ago I flew AA to GRU in C and had a few hours until my connection to Curitiba. They offered Arrivals service. Basically they meet you at the gate and escort you back to the Admirals club (which is in fact in the departure side of security), where you can take a shower, breakfast, etc. Later when you are finished they will escort you back to the immigration agents. One big advantage is when I got to immigration there was no line as everybody had already gone through from the earlier flights. Actually I remember the American Concierge who was taking me had to go find an immigration agent to stamp my passport.
Another thing that you may try is actually calling the Adminrals club in GIG and explaining your situation, they may have some way of taking care of you even if its not official policy.
good luck..