The best chance republicans may have is to make it clear that anyone here illegally voting in a national election will be sent to prison to serve a term and then immediately deported with no right to ever return.
That needs to be repeated over and over again by Trump, the GOP, state level, local level, etc. Make them terrified to ever think about it. Zero tolerance.
It may not stop them all but it may stop enough of them.
Trump should begin floating the idea of disallowing any Federal Funds to ANY State that allows a Non Citizen to Register to Vote by Executive Order. Watch them squeal when daddy takes away the credit card.
Illegals will never touch nor even see a ballot. Democrat activists are handling all of that complicated paperwork for them, in the background. Free of charge.