I guess I have a similar aspiration to squat ATG with bare feet or vibrams. The thought being the same as yours - if I can do that then I should be rock solid with weightlifting shoes. I think that by wearing shoes with squishy soles you are making things unnecessarily hard for yourself, though (so chucks or vibrams would be better).
I'm also starting to think that fairly minor adjustments to stance width, heel raise, depth etc can make a fairly big difference with respect to the movement. Enough of a difference that they might interfere with or slow the process of acquiring a smooth and automatic motor program. For myself, the main reason I'm squatting is to help me catch and stand up a clean and a snatch in competition. As such, I'm trying to set up as close to that as possible. Similarly, the best way to have a rock solid catch position with weightlifting shoes might well be to practice a rock solid catch position with weightlifting shoes. Once you have got that sorted then trying to re-achieve that with variations like no shoes might be a fun thing to do. However, YMMV.
Depends a bit on your levers and stance width...
My understanding is that in Oly Lifting you want to aim for your torso to be as upright as possible with the bar over your centre of gravity (midfoot). If you sit your butt back then your torso will have to lean forwards in order to keep the bar over your centre of gravity (so you don't fall over or lose the bar) - but then you are more likely to crumple under the weight. So, sit your butt down between your legs rather than back behind your legs. I think that is what Koing (and others) mean by that.
I think I'm doing a similar thing to you with respect to breaking at the knees rather than simultaneously at the knees and hips. I think the idea of breaking at the knees and hips simultaneously is the idea of setting your lumbar curve (breaking the hips in order to tilt the pelvis) at the same time as breaking from the knees rather than trying to set your lumbar curve on your descent after your knees have broken. But... Maybe Andy had something different in mind.
Was that what you meant, Andy?
I've been experimenting with setting my lumbar curve (breaking from my hips) before breaking from my knees because I'm still working on holding the hard lumbar curve through the ROM. I guess when it comes to dropping under the bar quickly (for snatching, cleaning) how one descends while squatting is fairly irrelevant, though. So long as one quickly hits a tight bottom position. So maybe whatever helps you maintain your lumbar curve (knee break, simultaneous knee and hip break, hip break first) doesn't matter so much. Dunno...
I'd be very interested to hear what others think.