Tom
I sort of agree with you re: Foxy. Firstly, you cannot effectively play the ground game off the tee. The numerous bumps and humps in the fairway make a slinging hook tee shot far too risky. Secondly, because of the interfering dune lines, unless you hit your drive to the left hand slot, you have to play the aerial game on your second shot (or lay up left). Thirdly, even if you do hit the ball left and long, the higher percentage shot is the aerial one, if you have it in your bag (I will grant that the ground game is a very robust option from that place, though). However, where the ground game does really come into play on the hole is on the 3rd shot. I would estimate that the GIR on the hole for elite golfers is no more than 10-15%. For players who are not a plus handicap it is probably less than 5%. So, the hole creates a lot of chances to practice up and downs! And, due the the great green siting, and the wild internal contours, and that great gnarly hump you mention that guards the right middle of the green, one's imagination can run wild. In this circumstance, the percentage play is the ground game, usually the putter. However, if you want to get it close, the lob wedge off the hardpan fairway is still the weapon of choice.
PS--as I've said on another thread, I think that the 4th is the best "ground game" hole at Dornoch (or anywhere else I have seen, for that matter).