Start making random audits of businesses tax information to figure out where some of these folks are working and make a few high profile busts. That's well within the authority of current law to do so. You don't have to bust every business; just pick an egregious violator and make an example of them.

How does that help? Many of them aren't working anyway, and stopping them from working just increases the burden on the communities they live in (because now they can't provide for themselves, so they need public housing and food, etc.).

Next I start flagging Tik Tok and social media accounts of coyotes (they have them) and start tracking these people down.

And do what, exactly? As you point out, these folks aren't hard to find. The reason they operate with relative openness is because the U.S. can't take any action within Mexican territory without the cooperation of the Mexican government.

Then I have somebody in Mexico have a quiet word with the cartels. Let them know that unless they help tone this down there the gringos might do something unfortunate.

If they were actually worried about the gringos doing something unfortunate, they wouldn't be in the cartel business. It's long been a far higher priority for the U.S. to stop the narcotrafficantes than it is to cut down on having too many impovershed Hondurans. As with the coyotes, they know the U.S. isn't going to do anything meaningful in Mexican territory - because the Mexican government will not (and cannot) be seen allowing the U.S. military to operate in their jurisdiction. They're a little tetchy about that, you know. They'd sooner agree to another round of "Remain in Mexico" than allow a foreign power to operate in their territory like that.