If you added Winthrop Rockefeller to this list, I might have gone with Winthrop - the most left-wing Governor of Arkansas.
Not really, at least economically.
Yeah, that's just a crazy claim. Faubus was literally a socialist, wasn't he? The fact that he was a racist doesn't exclude him from being left-wing, though that's always oh-so-hard for our forum Dems to come to terms with.
It's almost as if critiquing the Republicans and Democrats of the 1950s through 70s is hard because there were liberals, conservatives, people who were liberal in one area but arch-conservative/reactionary in another. Nowadays, the parties are more strictly aligned in most areas. Faubus would not be welcome in either party.