So... I was able to pry out the two shelves with a small pick tool. The upper one comes out easily as you gently pry from behind the top surface, near the corners. The lower one came out with some gentle prying near the lower two corners.
When removed, each shelf is kind of like a cup. I wrapped some duct tape strips on the outside of the cup to deaden the vibration a bit and reinserted the shelves back into the console. On a first test drive, the annoying rattle they were making seems to be gone. Took less than 5 minutes and was well worth it.
Red Green would be proud
