OK... I don't know if this will help anyone, but in any of the cases, above, is there any chance there may be some minor "plate lift" in the calipers?
The reason I ask is... I have brakes that did squeal like a pig - it didn't particularly bother me, I could live with it - on my commuting snotter S2. I figured I go through a set of pads quick enough if that is the problem... anyway as a result of some other work, I noticed I had some very un-even pad wear... I already knew I had some plate lift, overcome by the usual grinding of the pads (I have some shiny new calipers to be fitted now, but they are going on with new pads and discs all together). The un-even wear suggested one side or the other was sticking... looking at the discs, it was the side which wasn't worn, and sure enough, the pad was a pig to get out of the caliper. I hadn't particularly noticed it in braking performance, but after shaving a little more off the pad, all of a sudden the sqealing has gone (and braking performance has I think improved, not surprisingly). So... Could the squealing be the discs protesting at being "bent" by un-even pad pressure?
Looking at the way my plates have lifted, more away from the discs, I would say this would be worst with new pads... which could explain it improving for either hard application (forcing the pads to move whether they want to or not, and being worn away if they can't return) or, "bedding in" - i.e., being worn away over time to a position where the plate lift isn't so bad closer to the disc.
Not sure about this at all, but, if all else fails, or you have a set of pads you are about to bin because of squealing, there is little to be lost from giving it a go.
I have not, incidentally, noticed any "rattling" from loose pads. I have only covered about 50 miles or so so far, but when I say mine did squeal, I mean they really squealed, every time!!
Hope this might help some-one,
Regards,
Tref.