What about northern separatism from Mexico?
One of the members of the Mexico City Council was ringing warning bells about Americans moving into Texas. I think it was Melchor de Talamantes iirc, ITL he would most likely be working at heading that off. California was mostly an effect of the same process. A more stable Mexico would be able to better focus on the issues of the north.
This scenario is something I've been playing around with in my mind. It would make a very interesting timeline. I am not sure if they'd make itturigaray emperor, but it is possible. If anything at first New Spain would just be run by a supreme junta with Itturigaray at the head. Criollos wanted this cause they saw it as the first step in governing New Spain themselves as opposed to answering to a bunch of Spaniards who cared little for the colony's well being. So there will be struggle between the Peninsular elite and royalist Criollos against pro-autonomy Criollos. After a year or so I can see most Criollos favoring the new opportunities that an autonomous New Spain has to offer, and an attempt by Peninsulares to unseat Itturigaray. That conflict could lead to people like Morelos and Hidalgo to rise up in the name of the King in favor of Itturigaray and the Mexico City councilors. But it would be a much shorter conflict than the OTL war for independence. If the pro-autonomy side wins, they might be pushed closer to making a clean break. Even with better coinditions for Itturigaray, he is old. They'll want a new "regent" and maybe even a new supreme junta.
Iturbide was credited heavily by the people for independence at the time, which is part of the reason he had an overwhelming level of support for being crowned. Even when the political elite began turning on him, he still enjoyed immense levels of support from the common people. Mexican historiography has been very unkind to him (although he wasn't without some serious faults) and tends to ignore just how much of a cult following he had. Think Trump's MAGA crowd. The constituent congress feared a Jan 6 on steroids so they crowned him as a result of that. But since he most likely won't have such a large role in TTL's independence, that gets butterflied away. Without someone with that level of fame, Mexico will default to a republic barring any last minute European royals accepting the crown (which I find unlikely to happen but do enjoy reading a timeline on that).
This could happen by 1812, just in time for Spain to show up. Now OTL Pablo Morillo was despatched with his fleet in 1815 to Rio de la Plata to reconquer it, but he diverted to New Granada instead. ITL he could be sent to New Spain instead. There is a good chance he'd divert to New Granada, or he could go to new Spain with his 10k soldiers and his large fleet. There is also the issue of US/British recognition. The British recognizing Mexico is a hard one here. They did it in the 1820s cause the Napoleonic wars were over. But would they do that while trying to fight Napoleon in Spain and elsewhere? The US might be easier to get recognition from, but the US in 1808-1821 is um....useless aside from money and trade which is no small thing but if Morillo's fleet is parked on the Mexican Coast that could pose a problem, so recognition would have to come before 1815 and there's the war of 1812 that will keep the US occupied and unable to do anything.
If the supreme Junta gives way to a congress by 1810 Mexico has 2 years to establish a constitution, elect a president and congress and gain US recognition. If it succeeds on that forgoing anymore unity with Spain, it could probably seek recognition from Napoleon which would be troublesome cause of the British. It'll have to find a way to get both sides to see it as a neutral nation which could happen. By the time Spain is back and ready to attack, Mexico would have a some minor level of trade, and a much smaller economic problem than OTL Mexico. After that, I think holding of the Spanish is easily feasible. The problem Mexico would still face is the debate between federalists and centralists. This is basically what plagued Argentina so maybe its history could serve as a bit of a model for a timeline (in broad strokes). If Mexico starts off centralists, Yucatan, the northern territories and a few of the states like Zacatecas and Chihuahua might have an issue with it. If it starts federalist, you can expect the centralists to cause trouble with their military and church allies. I don't think Mexico is safe from internal conflict, although it would could easily see less conflict than OTL Mexico.
I don't think Santa Ana would be very prominent unless he gets lucky. A lot of the events that made Santa Ana famous by the late 1820s would be butterflied away. Since the Battle of San Jancito was the thing that won Texan independence (with Santa Ana's poor leadership and getting captured being the reason), I don't see a successful Texan revolution at least not until later in the 1840s with Santa Ana out of the picture. The French would probably still try to pull something like OTL Pastry War seeing as they did the same thing in Argentina. It would be hard for Mexico to be able to fight off the fleet the French sent, they sent a fairly large fleet to Veracruz. Mexico at best could fend off a land invasion, but would still face a blockade and probably still have to agree to pay up. Maybe not as much money in TTL.
An interesting concept would be Cuba. If TTL Mexico focuses on the Navy a bit more, it could at least be able to seriously threaten Cuba. OTL the UK was concerned about this prospect mainly because they feared Mexico would lose control of Cuba and the US or the French would take it. The French had similar concerns. The British tried to convince the Spanish to recognize Mexico's independence in exchange for Mexico abandoning its plans of invasion. The US was also interested in the matter. ITTL that might result in a more high profile conference that could have ramifications for the foreign policies of all those nations in the region.
Then there's the Central America question. Like mentioned, will Central America achieve independence earlier than OTL? Will Mexico send an army south to force out the Spanish? Does that mean an earlier annexation than OTL, and the repercussions? Since Mexico starts off as a "regency" and then goes into a Republic, would it hold on to Central America longer? Will its fate be part of the negotiations regarding Cuba? And if there's a failed Texan Revolution, American expansion will also look different which will also impact the political history of the US. And considering the role that that expansion played in sparking the Civil War, it won't be a minor change and this includes the US expanding west through Mexico. Just to throw something out there, what if this Mexico is able to encircle the US forces that land in Veracruz in TTL's Mexican-American war capturing the likes of Lee and Grant or even leading to their deaths?
There are so many interesting things to consider.
