Adding an update here, in case anyone else can help further the research.
Yes, I checked the book again and it says that some Burgos (Sefardies) went to Smyrna (Izmir, Turkey) after the expulsion. Falcon del Burgo, interesting! The Falcon surname is in this book too and it mentions Falcons going to Toledo, Roma, Livorno, Bordeaux and Amsterdam. The surname Falco is here too and mentions Sefardies going to Torina, Gerona and Milano. I'll attach both pages to this email/post. Book source: "DICIONÁRIO SEFARADI de SOBRENOMES Inclusive Cristãos-novos, Conversos, Marranos, Italianos, Berbères e sua Historia na Espanha, Portugal e Itália"
I am in the process of figuring out the migration pattern of my family with this surname. It could be possible that after the expulsion they spent a little time in France and/or England then went to the Americas or... after the expulsion went directly to the Americas.
Here's the variation of the surname that I've encountered thus far:
Gallicized: Borge, Borges, Borja, Borjas, Borjes, Burgos, Burguera, Burgues, Bourgeois, burgeois, burges, borgûes, bourges, borjois, Bourgeois, Bourgois, Bourgeoys, Bourgeot, Le Bourgeois, de Bourgeois, Bourjois, Bourgès, Bourgeix
Anglicized: Burgess, Burgeis, Burghersh, Burges, Burgesse, Burgar, Bergiss, Bergess, Bargess, Bargeis, Bergeus, Burgeus, Burgeuss and many more. Borges, Borgeis. Variations in the spelling of the surname include Burges, Burgiss, Burgis, Burgise and Borges.
Vi Burgo Seeking geographical origins of Burgess (anglicized) / Burgeois (gallicized), original name "Burgo"