Charge them all, including those who paid them.
Anyone in the country illegally gets deported. We have no obligation to deport a criminal to a country he claims to be from, so deport him anywhere.
Do it by lottery on television. It can be like "The Running Man".
Maybe he'll go to Ukraine. Maybe he'll go to Afghanistan, Iran, or Haiti. Place your online bets before we spin the wheel and find out.

IMO, the non-indelible dye further proves govt isn’t serious about the problem(s).
God knows the wringing of hands/gnashing of teeth if the termination of the welfare state (THE fix) would cause govt from dog-catcher to the Pres.