The city of Antofagasta in northern Chile, was founded by the Republic of Bolivia in 1868. The founding damero can be seen on a map of 1869. It consists of square blocks, rotated 45 degrees respects the cardinal points, the square is at the center, and is surrounded by eight blocks divided into lots. To the southeast, south and southwest, the damero is extended in a row, or seven more blocks.
I don't know about the specific context of Latin America, but generally after Savanah (the harbor city in USA) was designed in grid system with 90 degree angles, using the orthogonal grids became more popular and later semi-grids were designed, using the 45 degree angles and traces of the existing net from the context. It was easy and fast to design a orthogonal grid, less expensive to build and easier to handle comparing to the organic grids which was a better chance to make the development happens faster. If you could not find something specific for your context, maybe it is not a bad idea to look at the same time frame(a bit earlier) in other countries or looking for similar examples and checking if those reasons could be applied to your context. Hope that helps.
About American cities with Spanish influence, I am studying an article by Richard Sennett, entitled "American cities: orthogonal plan and Protestant ethic". This text says something that I very much agree, especially if it relates to found a city in the desert: "In modern times the grid seems to have been a plan in place to neutralize the environment".