You forgot, "Can't You Hear Me Knockin" with its amazing jazz sax/guitar bridge.
Other Stones country are Wild Horses, Tumblin Dice, Sweet Virginia, Country Honk. Nothing gets more country than "High and Dry" on their Aftermath recording. That was one of if not their best albums. C'mon man.
LOL, I think Martin Scorcese owes his career to that album.