I am sympathetic but your idea 1. is obviously unconstitutional.
As for the second, there should be no thought of any amnesty for illegals. No reward for illegal entry. Those illegals who vote illegally should not just be barred from future citizenship, they should be prosecuted criminally, then deported. Those who have been convicted of any crime more serious than a traffic ticket should be barred from entry.
My thinking is that if a gang of members in congress demanded checking voter roles and charging felonies, the amnesty talk would maybe stop in a hurry.