The Saturday airport drop and having Castle Stuart on the books for Monday will force you to do a lot of driving, which you probably already knew. Any chance you can move CS to Sunday, playing Gleneagles or Prestwick en route on Saturday? That would open up Mon to get to Fife Tues to try and get on the Old Course, which - closure aside - should be pretty doable in early October. If not, consider Brora - 1 1/2 hours past Castle Stuart - on Sunday.
And, if time permits, try Dunaverty on Friday after playing Machrihanish. You'll be glad you did, it's only a 15-20 minute drive from one to the other and the 4,800 yard course can comfortably walked in a little over two hours.