Hrmmm, that sounds exactly opposite what rim brakes call for. They call that wedging “toe” on rim brakes and it keeps them from resonating with the rim. But I have no experience with disc brakes so can’t really say anything specific about them.
Yes similar but different situation. Small creaks can be so frustrating to find and repair because the movement creating them is so small. I hope the solution to the creaking is found and posted I enjoy a good mechanical mystery.