I think the tee shot on the Eden is the single shot I anticipate the most when playing TOC. Which says a lot for me - it's that good. Mind you, there's a pretty decent Eden on the New Course in St. Andrews as well - no. 13. It's a bit shorter, and obviously there's not the double green, but I'm quite a fan of it.
ChrisB (and Bill), with the pin behind Strath Bunker, I would almost always try to fade the ball toward the hole - the general lay of the green slopes to the right, toward the 7th hole, and if you can start your shot at Hill Bunker, you can just about get your ball to do a 180 and trickle back toward the hole. Mind you, it doesn't sound as though that was an option for you.
Cheers,
Darren