Sorry if I bring tumult to such an orderly debate, but I can't help adding something I read at Saudades da Terra, of the Azorean priest Gaspar Frutuoso (1522-1591), volume IV:
Page 51: "The Gagos and Bocarros are from the city of Beja, wherefrom Luiz Gago came to this island; he was the son of Estêvão Ruiz Gago, born in Beja do Alentejo, called do Trato for being a rich and powerful man and to have treated with the King at Mina, Caboverde and other places, where he used to send his ships; also called Raposo, for being married to Catarina Gomes Raposa. He came to this island, where he had a big house and family and became its richest man.
Page 52: "Jacome Dias Correia (...) had from his wife Breatiz Roiz Raposa the following sons: Jordão Jácome, Barão Jácome, Dona Isabel, wife of João Silva Canto of Terceira island and Catarina Gomes Raposa, who was the wife of Manuel Vaz Pacheco; and Aldonça Jácome, the eldest, who was the wife of Agostinho Imperial. Jordão Jácome Raposo, first son of Jácome Dias, married a second time Margarida da Ponte, daughter of Pero da Ponte, the Old, from Vila Franca, e of Ana Martins, daughter of Martim Anes de Souza, and of their daughters two are nuns."
On Jewish origin, I found the following at the index of volume II: "Captain Jordão Jacome Raposo, married to Margarida de Bethencourt, great-grand-daughter of the new-christian Gaspar Dias, page 76."