A trim shop solved the question. Although it sounds like there may be other approaches (?depending on the year of manufacture), my '87 560 SL's is thus: Lift up on the forward (front) edge with each hand, and then pull the shelf forward and free. There is a horizontal, center located, clip on the back wall of that compartment that the shelf simply slides into, and then in the front drops into two simple verticle clips, each near the semilunar hand hold cutouts.

I could have figured this out myself, had I been willing to force things a bit, but the cost of repairs of these things is daunting.
So, I post this for the benefit of the other members who tried to help me out.