You haven't removed the deadly Columbian exchange though.
Why do they always overlook that part?
The Columbian Exchange wasn't some one time event either. The diseases involved were still wiping out native groups in the 1800s. It wasn't as if Amerind societies could survive the first pass and everything would be fine afterward.
I'll second the previous suggestions of a short war of independence followed by a fairly stable, fairly competent, somewhat authoritarian monarchy/empire followed by a general liberalization. Our preoccupation with representative governments is nothing more than our 21st Century Western liberal democracy cultural blinders at work.
The American Revolution only succeeded in eventually setting up a republic, albeit it one with voting restrictions that seem drastic in our eyes, because the peoples involved had already been governing themselves for the better part of a century and had mostly immigrated from a culture which had operated under a constitutional monarchy before that.
The idea that Mexico could jump from an authoritarian colony directly to a stable, working, representative form of governance without first developing the necessary cultural foundations is nonsense. France wasn't able to do it in 1789, so why would Mexico be able to do it in the 1820s?