Are the countries on the continent of South America not generally considered a part of Latin America? Because there are other options from Santiago, Sao Paolo, Rio, etc. to Tokyo. Some of the options are on Air Canada, with a stop in Toronto which avoids U.S. airports but presumably not U.S. airspace so there may still be some additional scrutiny at departure.
You don't actually have to go all the way to a South American city, Panama City has Air Canada flights to Tokyo. It looks like the other carriers (Emirates, KLM, Turkish Airlines) have stops in a South American city first. The Air Canada flights aren't much more expensive but the European & Asian-based carriers are much more expensive than the flights with stops in the U.S.