So, this weekend I took the top panel, removed the grill, replaced the thin filtering foam with foam board. I then took the front grill, and put matte black vinyl between the grill and plastic bezel. This is the sound stopping layer, I still need a sound dampening layer all around.
I've cut the foam board for the hardware side, the back side, top and bottom. I need to get myself some two sided tape to glue the foam to the foam board.