I'm rather interested in TL's with surviving Native American civilizations, hell I'm a bit of a sucker for them. One thing is what happens next. In the few Incas-survive TL's I see, the Spanish don't roll a bunch of 6's in their attempts to conquer the Incas, and the Inca adapt enough to European tech to hold the Spanish at bay. Invasion becomes a rather costly idea to the Spanish, and the Inca ally with a European power looking to screw over Spain, while making profits off of their silver mines.
Now, let's say that they've survived as the only (or one of very few) surviving native states, all the way down to the Industrial Revolution. Could the Inca pull a Meiji in this case?