I like the "follow you eyes, let your body catch up naturally" idea. I think your body will perform fairly well when its all natural. but I've found that if I do not practice using both my hips and shoulders, that if its a long spread of targets, ill start to throw rounds towards the end. I end up squaring up the first target, and by the end I'm in a odd angle. Then that throws my recoil off slightly. I think in the end it all comes down to practice.
As far as up and down goes, I cant say I've come across a stage where I have had to worry about that. So I personally have not practice for it in any manor. I would guess though, that leaning back could only be done but so far without compromising a well planted stance.