"....I'm pretty sure the pad springs were okay...."
Doesn't matter, you can get ill fitting pads, the 'pad pin hole' may be a tad larger than other pads.
Add that to being cleaned, and it's free to rattle.
Pad springs are held in the middle, not the ends, so can still pivot with a loose pad!
Check there's no groove marks on the pad pins as well.
More people are born because of alcohol than will ever die from it.