If you want to build up against shared walls, be sure to remove the drywall from those walls first to avoid a triple leaf situation.
Frame the new walls a few inches from the existing studs. Run your own joists to completely decouple things. Insulate everything and double drywall with Green Glue. Box around ANY penetrations like switches, hvac, outlets, can lights, etc. Use a solid core door and add seals.
To prevent flanking through the concrete slab to the block, float a floor. Dri-core works great and will also help with moisture and keeping things temperate.
Foam will not soundproof anything. It's purely a dampener of interior reflections - and not a very good one - especially for something very dynamic and low frequency heavy as drums.
Lead Acoustical Designer
I am serious and don't call me Shirley.