"...... there's nothing about his getting his ideas from the native peoples in it ..."
Right, there is nothing about Indians, which is why I asked:
"Is the International Explorers Society (I.E.S.), which according to Time in 1975, was a travel-oriented organization based in Coral Gables Fla, still around? Are the researchers still around? If they are, have you asked them for their evidence concerning the documents at the University of Coimbra?"
You wrote that you "...had no way to prove or disprove the story", so why not simply ask them to provide the evidence for their claims?
If they are still alive, judging by their photos taken when they 'flew' the balloon, they will be in their 70's or 80's today, so you might still get some valuable info concerning the Coimbra 'evidence'.
You also wrote: "Considering how he stretched other evidence I take it with a grain of salt."
That's understandable, but unfortunately, this piece of 'evidence' which seems to have been important to their theory, no matter how dubious it seems to be, still remains unresolved.
Judging by the evidence you have presented so far, I don't hold out much hope that any evidence will emerge to substantiate their claims that the Jesuit priest got his idea from the Indians, but it still should be checked out, and IMHO, the best way to do that initially, would be to try and contact the researchers if they are still around alive and kicking.
CT