This is a very helpful thread! Apparently this type of noise -- although it sounds like something terrible has happened -- is often quick, easy (and free) for a householder to fix using no tools.
In my case the glass turntable and the support ring with the three little wheels were fine, and the sound continued when I removed them.
But the coupler - that approximately 2"plastic part with three legs that engage the bottom of the glass turntable - had been pushed down and was tight to the metal floor of the oven. I pulled it up an eighth of an inch or so and the sound was gone.
Interestingly, when I replaced the glass turntable on its support ring, and pressed firmly downward, the coupler did not move back down. It is apparently designed to ride above the metal floor of the microwave with a comfortable clearance. I have no idea how we managed to drive it down against the metal.