You're dealing with an unsophisticated thuggish bully. You need to call their shit in a way that makes them look weak, and punish them for trying shit but still let them slink away. Incentivize shutting the hell up and never mentioning you again.
If you let them shoot back, you need to kill so fucking many to end it. If you challenge them they have to escalate.
If you kill them, then lie about it brazenly and obviously. they're punished, and calling you on the lie makes them look weak, costing them face on both sides of the border. Literally any evidence they have or claim to have can be safely denied; their credibility hovers around nil; it's genuinely a weird political moment when one of them says something that's just true. You'd get Luigi nangione type 'he couldn't have shot that man, he was at my house' type testimony from at least half the country.
It's the best chance to avoid the need for large scale killing. Long term you're saving American lives if you do it all quick and clean(ish). Not that they're not just gonna get spent on some other dumb shit, but it won't be on you. Return the bodies when the regime falls and apologize for the necessity of killing them after the regime falls if you really want to be decorous about it.
Yes. So many. Everyone involved in this decision, on both the legislative and corporate sides, needs to get the fucking wall.
But it's new Orleans, so some of the difficult to emotionally comprehend number of deaths it causes might at least be funny.