A week before the invaders arrive, completely shut down the border and flights from Mexico, and seize all cash transfers. With tens of thousands of trucks, and rail cars stopped, perhaps the Mexican government will take some action.
Sounds like a remarkably good strategy, especially seizing the remittances—but at that point all the Mexican government could do is try to halt any FURTHER migration beginning within their borders. You mention the timeline of “a week before the invaders arrive” and thinking about it I do see how the actual migration could be perfectly monitored through a variety of GPS type surveillance, so that we’d know EXACTLY where they are and in what numbers, and who is bringing up the rear, so you do have a good point there also.