Out of curiosity would it be a better idea to line the floor with soundblock board and sheet? I can see what you mean by the previous idea making a giant drum skin.
A week late..but Rod never replied, so
, at the risk of giving bad advice...I'd submit the floors are ALREADY a drumhead. Simply adding a small amount of mass..ie..soundblock board(what ever that is?) won't do anything appreciable.
The thing is, you need a MASSIVE slab..decoupled from the rest of the structure by virtue of calculations. And this is the reason the existing building MAY not be able to support it. My less than scientific observation..ie... $.02