"Put all your eggs in one basket--and watch that basket!"
This doesn't really apply exactly since Mexico has no choice--they have a border region that's pretty much doomed to repeat the circumstances that lost them Tejas--the Los Angeles zone* is right up against British California and particularly a part of it likely to get a fair number of settlers, and the kind of people who settle the middle coast stretches will quite naturally want to move in to what the Los Angeles Times of OTL took to calling "The Southland." A big difference between The LAZ and Tejas circa 1800 or so is that Mexico already had a fair amount of settlers and political hegemony there--but not much compared to what is going to be rushing into British California. To be sure Gold Rush BCal is going, as OTL California came to be for some time, to be centered on the Bay Area. But the question of whether the circumstances that led to losing Tejas will repeat or not is out of Mexico's hands; the question is, what can Mexico do about it.
Meanwhile they have another critical border zone, Nuevo Mexico, which has a definite population zone with a fairly long history of being part of the Mexico-City centered system (under New Spain and now Mexico) but on the other hand, a sometimes unfortunate one of unrest. The Pueblo peoples and other Natives, notably the Navajo, who have the potential of operating more like a Western nation than most Native Americans had, are another possible crisis.
Which, the anecdote says, is translated into Chinese as "unavoidable opportunity." If the Mexico City regime(s) is/are feckless, incompetent, distracted, or wracked by national crisis, there's a serious likelihood these two border zones will drift out of the government's control.
Trying to close off the zones to British contact might seem like a solution, perhaps tried at one time or another in the coming decades and century. But it will be a difficult one. Easier in the case of Nuevo Mexico at first, as the northwestern reaches of Tejas and Louisiana probably won't be attracting much Canadian attention--they'd be more concerned with NM's far northern border, as it is in the way of a decent direct overland route to BritCal. But the problem of controlling NM is one of keeping the Native peoples there more or less on board; restricting them may be resented. In Nuevo Mexico, a gradual devolution of autonomy to the Native authorities may actually be the best policy; the locals won't want to encourage a lot of Anglo immigrants to swamp themselves. But autonomy has its perils from the Mexico City point of view--the upshot is, the central government will realize it has to keep an eye on that border zone, and steer lightly but carefully.
And that a similar policy is in order in the Los Angeles Zone. Building on the existing mission-based Hispanic hegemony there, they need to encourage the right kind of immigration there, and manage things so that it grows in a fashion that keeps it attached to Mexico. The more they grow that central zone of Californias, the more BritCal settlement in their southern border region is encouraged.
Yes, they will run into some water limits. To be sure, the Colorado River runs entirely through Mexican territory and its mouth is in Californias by Nugax's map. Nugax by the way has suggested that instead of the Los Angeles Zone, regions around the Sea of Cortez will develop instead. But those regions never came to much OTL, even though New Spain had control of them long before they sent the mission chain north along the coast to secure OTL California from the Russians.
Mexican Los Angeles will be in no position to extort the Owens Valley waters to be sure. But OTL Southern California developed without these diversions until the turn of the 20th century. Today, according to this, the Los Angeles Aqueduct delivers "half" the water used there.
Clearly if no water comes from the north at all, the potential for development is more limited. But clearly it wouldn't be a matter of getting no water at all. I'd think the Los Angeles region would get at least as much water as it currently does from the Colorado River, even if Sonora and other Sea of Cortez development is somewhat greater.
So, an alternative to Mexico either losing the Los Angeles zone completely or keeping it by rigorously closing the border, thus dooming the region to underdevelopment, might be for the Mexico City government to get used to the necessity of fostering, and closely watching, development of this border zone (and Nuevo Mexico) so as to keep pace with developments on the British side, and to carefully engage the British in investing on the Mexican side while watching to make sure their incentives are to preserve the status quo rather than to adjust the borders to gobble them up. It would be a tricky balancing act, getting the right balance of Mexican versus foreign involvement, keeping the border zones interested in staying in Mexico, while diverting enough profit and revenue southward to make this look worthwhile to the rest of Mexico. But if the Mexican government gets used to this necessity of life, it could get easier. Mexico as a whole profits, and is drawn away from hostility and resentment toward Britain toward a commitment to active partnership. This in turn would make the task of engaging with British enterprise while securely holding the border zones easier. Cross-border enterprise, and migration of people both ways across the borders, would become easier and more routine.
Under those circumstances I may yet get my largely Anglo-influenced but still Mexican Los Angeles, a great world city attracting immigrants from around the world, culturally part both of Mexico and the Anglosphere.
They might even get a fair amount of that northern Californian water; if there are a lot of British subjects and expatriates living in the Los Angeles zone of Mexico and participating in profitable enterprises there, they might have influence to get the British California government to consider selling water to Mexico. Probably not the excessive diversions of OTL! Mexican LA would be dryer than OTL Southern California. But not, I think, dehydrated to the point of death.
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*I can't think of a better name; calling it Southern California as per OTL is all wrong for this timeline, calling it "middle Californias/North coast" is awkward
).