Final ceiling decision - please help

We're about to start building a 10' x 12'10" room within a room (23' a 17') in a residential attached brick building in NY, right onto the concrete basement slab. Assume we've designed the within-room pretty well. The existing ceiling height is only 7'10". The ceiling of the within-room will be 3 layers of 5/8" sheetrock under 2 x 4 18 gauge metal ceiling joists in pairs back to back 16" OC, and 3 layers of Owens Corning 703 on top, so one layer is above the top of the ceiling joists, and an inch or so of additional airspace under the current existing ceiling. The main noise we're dealing with is the upstairs neighbor's booming footsteps, not much noise on the side walls. Here's a description of his floor from the top down to our existing ceiling: hardwood floors, plywood subfloor, attached directly to 12" metal C-joists, z-bar attached to the joists, old 1" Thermafiber in the z-bar space, one layer of 5/8" sheetrock, another z-bar, another layer of old 1" Thermafiber in the z-bar space, resilient channel going at right angles to the z-bar, and a second sheet of 5/8" sheetrock. Here are our options: 1. Current plan: add 1 layer of 5/8" sheetrock directly onto the existing ceiling to add mass. Build our within-room under this. 2. Or this more difficult option (we're little old ladies and we're doing the work ourselves): We're concerned that the existing ceiling already functions as 2 leaves. So, demolish the ceiling, then add mass by screwing 3 layers of 5/8" sheetrock directly to bottom of the sub-floor above, between the joists. Then build our room. We would love not to do this nasty job, so we're trying to get a sense of how much difference it would make. So sorry, I deleted the sketch, it was a mess. Hope you can help us decide.