If we can pay them welfare, and pay for their healthcare, and pay to educate their children...we can damn well afford to deport every last one of them. And no, they don’t all have to be rounded up at once. You deport them when you find them, and in the meantime you cut off every single benefit available to them—up to and including lifesaving emergency care—to make life here so untenable that they will begin to leave of their own accord. And actually, we can round up and deport mass numbers. We did it in the 1950s with Operation Wetback, back when it was much easier for someone to stay hidden.
None of what you propose has the support of “compassionate” “American” people.
All correct remedies, but who is going to do it? First we have to win elections. The way our system operates, elections have huge consequences. Snow in July has a better chance than Obama & Holder doing what you wish. Wishful thinking and posting on boards is not going to do it. Do everything possible to help elect the right kind of candidates. Send every dime you can spare to them. Wear out your shoes and telephone. Become a precinct captain. Been there, done that. More people needed to do the same.