As long as both houses of the state legislature agree, I don’t see where SCOTUS would have a problem. It is a well established principle that a legislature cannot bind or restrict a subsequent legislature from exercising its power. So even if a previous legislature passed a law saying the electors can only be chosen in a certain way, that cannot bind a current legislature, and they would be able to change that with a simple majority vote.
Not if the state constitution says laws have to be signed by the governor.
They may try to ignore the existing law but the constitution dictates how new laws are made.