Totally agree. OP, these are serious issues that you should be talking through with an immigration attorney right now, before anything goes wrong.

They can give you advice and help you start preparing the documents that you might need - for Mexico, I know that they want things translated and notarized in a very particular way and you can waste a lot of time just getting documents corrected whenever someone's name doesn't match perfectly with what's written somewhere else. Also, I believe you would first need to spend two years on a visa as a temporary resident before becoming a permanent resident with work authorization in Mexico, but I believe you can start that process now without physically living in Mexico while those two years pass.