Sorry but I'm not seeing Mexico as an effective solution.
What kind of visa do you plan to use to live in Mexico? A tourist visa is short duration and wouldn't allow you to work, so how do plan on staying two years there? To get a residence visa you would either need a job or show sufficient funds to not be a drain on the state. When I worked in Mexico my company had to jump through hoops to get the correct visa issued, and that contract was with the government.
There is also a very good chance that Mexico will learn of your visa problems during the application process, and your application could well be denied.
You would face similar problems in the rest of Latin America too.