I've gone PDX-GRU several times. You may be surprised to learn, as I was, that KE (Korean) flies non-stop from LAX. Every other time I've connected in IAH or ATL or JFK. But the latest time, just a month ago, I found the cheapest was KE.

I had an empty seat on the way down. The return flight was full, but at least they had a rare day time departure time. Got into LAX about 10:PM. That alone would have made it worth it. But it was also probably the best service I've ever encountered. Highly recommended.