Hi Kevin,
Welcome to GS.
You can raise the ceiling by lowering the floor. Digging down the basement floor and pouring a new slab would solve this problem. - How much did you want to spend on this project?
I would recommend a minimum ceiling height for recording drums to be 9 feet. At 9 feet, you will need an absorptive ceiling over the drums. So, if the ceiling is lower, I would recommend heavy trapping above.
If you didn't need the isolation, you could fill between the joists with building insulation (attic blanket) and cover with fabric. - This will be close to 9 feet to the hard 'ceiling' surface (bottom of floor above) with heavy trapping.
You do not need to float your floor. You are in a basement. The slab is on the earth which is a good damping material.
Cheers,
John