I like those slate slabs! I wonder who would have them around here in So. Cal.
For those who don't have kids, I highly recommend trying components with the lid/cover taken off. For years, I tried similar things trying to "damp" the chassis, including EAR damping material, sorbathane, rocks, sandboxes, etc, etc.
In the end, when I took the tops off and just concentrated on the bottom shelf, things sounds a lot better. A lot more open sound, and definitely a sense of boxy/resonant character disappears.