Myself, would put up an actual border fence. On the US side, make regulations so onerous as to initiate self-deportation.
That would involve hiring probably a hundred thousand officers skilled in the art of combing through suspect business records to weed out the illegals and fine or jail the business owners.
First of all, it wouldn't work. Conservative economics... we make it desirable for them to be here. They will come. No matter how they get here.
Second, if there was any political will to do this, it would have been done.