It really is hard to organize a boycott, but several individual incidents of putting pressure on a business may get the owner concerned. If you owned a business and someone called to warn you that he was looking to get you shut down, would it worry you? Especially if you were actually hiring illegals? This may be an opportunity for a legitimate business doing the right thing to damage a cheating competitor.
Just as there is a "Better Business Bureau" and a "Seal of Good Housekeeping", or" ISO9002" couldn't there be an organization that investigates and awards "Immigration Good Citizen" certifications to stick on business windows?