I would fly directly to Iguacu. It is amazing. Have a guide pick you up at the airport. Use trip advisor to find a guide. It is well worth it. You should get there in time to see the Brazilian side of the falls and do the Macucco Safari to get up close and personal to the falls.
In regard to the Argentine side, if you are an American citizen you will have to pay a reciprocity fee of $160 each (paid online before you go). Personally, having been to the area 3 times, I think it is worth it. If your guide picks you up early, there should be plenty of time to make your flight back to GRU. Don't try it without an experienced guide.
If you don't want to pay the reciprocity fee and see the Argentine side, then have your guide pick you up early and see the Itaipu area including the Animal Reserve. You will learn a lot about engineering and conservation.
Good luck and if you have any questions PM me. We went the first time in 1991 way before a lot of building. It is an amazing place.