The case is about legal residents, illegals are never even mentioned.
your best alternative is H.J. Res. 42, sponsored by Rep. Ron Paul of Texas, to amend the Constitution to deny citizenship to individuals born in the United States to parents who are neither U.S. citizens nor persons who owe permanent allegiance to America.
No need for that at the moment. The best and quickest process at this point would be for Congress to exercise its legislative authority then let the USSC hear it when it's challenged.
Actually, the lower courts had held he was not a citizen and therefore an illegal alien, so it is at least dicta that any such child born in the U.S. is a citizen. Like I said, your best bet is to get another Amendment.