You are absolutely correct.
May I add one thing to your list: Tax all remittances to Mexico.
BTW, some economists are saying that when Mexican wages approach 35% of US wages the flow will slow down.
We can accelerate that happening by the imposition of the tax and by removing incentives.
Frankly they can tax all money transfers back to Mexico at 75% for all I care. I want those funds plowed back into our economy, not theirs.