PC: Mormon New Mexico

According to this map Pervez Hoodbhoy posted the Mormons did move towards New Mexico during their Exodus along with Utah. Furthermore parts of what later became New Mexico and Arizona were claimed as being part of Deseret.

So I'd like to know if it were possible for the Mormons to be granted land predominantly in New Mexico as their "homeland" and how this could happen (and what exactly were the reasons for Utah to be chosen anyway)?
 
There are some Mormon towns in the Four Corners and Arizona border areas of New Mexico.

The Mormon Battallion (a US military unit) was also marched through New Mexico on its way to California.

These two facts don't add up to much potential for Mormons primarily settling New Mexico.

The big problem is that New Mexico already had settlers. Brigham Young was looking for unsettled land.

Here are two possible but unlikely PODs. First, have the US Government give heavy incentives to the Mormons to settle in New Mexico as a strategy for 'americanizing' the place.

Second, postpone the Mexican War, have the Mormons work out a good modus vivendi with the Mexican government, have California pull a Texas and become independent and then part of the US, and only then have your Mexican War break out. If the principal US war aim is a good route for a transcontinental railroad, you might plausibly have a peace treaty where much of OTL Arizona and New Mexico stays in Mexican hands. Then have the Mormons decide they'd rather live under the friendly Mexican government than the hostile US government (maybe have some nasty fighting between Mormons under the Mexican banner and US troops) and have a savvy Mexican government wanting to shore up its northern outposts offer the Mormons settlement rights throughout New Mexico and Arizona, and you might have New Mexico be the focus of Mormon settlement, albeit as Mexican states, not as US ones.
 
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