Regarding using sand. This is not something you can do haphazardly, it will add significant weight to the structure and would have to be adjusted by the engineer in the plans to support that weight. So definitely DON’T do it without proper consultation. I have seen it used but in a subfloor that was built on top of a concrete slab with the joist of the floors on rubber pucks to isolate from the concrete sand filling the void. It worked extremely well. But in your situation likely would be cost prohibitive as well as possible building code issues.
Unfortunately your options are limited. Filling that cavity with Roxul safe and sound will help, cross bracing (blocking) the joists to prevent bounce in the floor will help and won’t cost a lot extra. Adding some sound isolation mat under the carpeting will also help (but definitely not cheap). Something else to consider is a product like Green Glue (http://www.greengluecompany.com)
which you use between layers of plywood (or other flooring) will help with dampening the sound vibration (also possibly cost prohibitive).
All of these will help but you can only go so far in dealing with the floor suspended. Airborne vibration will mitigated mostly by what I explained above, it’s the flanking vibration (from amps, drums, jumping, stomping feet etc.) that will transmit through the floor the most. An isolated drum riser, getting amps of the floor on stands with a small footprint on some vibration barrier etc. will help with that to a degree.
Also follow Paul’s advice and read that book, and the books I mentioned earlier, it’s a lot to absorb especially if you are more interested in making music than learning about acoustics, but I hope you get something out of this that is satisfactory for your application.
Keep us all posted on your progress.