I will second (or third) the above ideas relating to the replacement of the glass shelf. I experimented pretty extensively with 1/2" glass as shelf material and it is not bad (better, in my opinion than marble or granite), but it is pretty expensive. I have a target rack with MDF shelves, but use a vibrapod sandwich exactly as you do. I was using 1/2" glass, but after experimenting with a simple 3/4" maple cutting board from Home Depot ended up with that. Spend $15 on one there, or at Bed, Bath and Beyond and I virtually guarantee your problem will disappear; my guess is that 1/4" glass would be pretty awful as shelf material. You may also find that using anything metallic under the CD player will end up giving you a "metallic" sound or one tilted toward the high fequencies. I'd experiment with the CD player sited directly on the cutting board, and possibly with vibrapods between the board and the player as well. If you like the sound, you could investigate going with thicker maple perhaps, as some around here have, but I'm kind of cheap and have never felt the need to upgrade the "cutting boards".
