My understanding is that states already have the ability to appoint presidential electors however they want. No need to repeal any amendment, if a state wanted to do things differently in that regard.
My proposed elector appointment algorithm is as follows. For each elector seat, summon 20 grand juries according to standard methods (distribute across various counties, weighted by population). Each grand jury spends a day getting to know one another, then appoints one member as a representative using approval voting. The 20 representatives from the 20 grand juries form a secondary grand jury, which also spends a day getting to know one another, then appoints one member as a representative using approval voting. This produces 1 elector. Electors serve 8-year terms, staggered so that their appointments occur midway through a presidential term when emotions are relatively placid.
If you persuade a few big swing states to adopt this approach for appointing electors, the nature of the presidential contest changes dramatically.
This is more along the lines of how the presidential elector system was supposed to work in the first place. Presidential electors were supposed to be leading individuals of the community, not otherwise involved in politics, exercising their independent judgement. That's what the founders intended.