Bumping this because new information has come to light. The Kaiserreich mod for Hearts of Iron IV has
made me aware that the Spanish Empire has the
Dukedom of Moctezuma de Tultengo- a hereditary title for the descendants of Moctezuma, who I didn't even know existed. So that means Mexico actually does have at least three hereditary lines of note that did rule as monarchists- Iturbide, Hapsburg, and Moctezuma. So how would this play out? An interesting inversion of
this post, I think:
1) old dynastic line (Iturbide - the original Constitutional Emperor)
2) branch of old dynastic line (Hapsburg - adopted Iturbide descendants for legitimacy, but did not plan on actually passing the crown to them)
3) different dynastic line (Moctezuma - completely unrelated to the major houses)
Of course, the funny thing about this is that the Hapsburgs are as venerable- and alternatively, as despicable- as the Bourbons and Moctezuma is the oldest line of the three on the continent. But hey, imagine if there was a scenario where a Moctezuma de Tultengo who was a really good fighter and strongman was crowned king of Mexico because no one wanted to deal with dueling Iturbides and Hapsburgs, and also because he conquered it all.