Any advice would be greatly appreciated
Stop while your ahead

just kidding.......
First, by vocal booth, I assume you mean an acoustically isolated and "soundproof" enclosure. So with that in mind, here are some considerations. This is not to tell you how....yet. As you are in apartment, you already are dealing with a handicap. But since you have all ready permanantly altered the finish on the ceiling by contact cementing padding material, which I assume is foam, I also assume you know very little in regards to sound.
I covered the parkay floors with commercial carpet withcompressed padding underneath and I put some of the padding on the ceiling with contact cement (I want to respect the solitude of my neighbors).
What gives you the idea that padding will help the concrete ceiling with its ability to attenuate sound? Foam will do practically nothing to stop sound from transmitting through to adjacent spaces. If anything, it will suck up the high frequencys in the room.
and a floating platform for the control area.
What for? If there are no barrier walls and ceiling, what does it do? Nothing but elevate the engineering position. Lets move on.
Self contained vocal booths assembled in an apartment is a tough proposition, period.
First off, let me say I am no expert. But I do have so info for you to consider.
Many people build and post descriptions here of quasi soundproof vocal booths and are happy with the results. However, IF you are talking about a booth with a sound transmission class appropriate for recording in an apartment, I would suggest you find out from your neighbors if they can hear you in the first place, as you have concrete walls and ceiling, and quite possibly the floor also. If vocal work is the only thing you are trying to isolate, it would seem to me, the appropriate solution depends on how loud the sound is the neighbors are hearing, as well as the environmental noise of your apartment and surroundings.. Does that make sense. In other words, why build a booth with a STC rating of 45, when you only need an STC of 30. It works like this. For EVERY db of isolation increase required, it takes TEN TIMES more ability of the isolation structure to keep sound from transmitting through the booth shell or structurally to and from the room structure.
Here are some of the other considerations.
Weight. vs structural floors. Point loading can create problems as even a 6'x 6'
booth is extremely heavy, and actually could compromise the existing floor structural integrety.
Verify your floor structure and material. It has a bearing on various things. Steel studs are light weight, but sheetrock is not, and if wood stud, floor and ceiling joist construction is used, the weight added is significant. Not to mention the booth floor and exterior sheithing. Add a person who weighs 150 lbs....well, think about it.
Air. Sound proofing is airproofing. Nothing is worse than telling a singer not to breath while they sing. Ha! Therefore, to vent it, you must penetrate the wall or ceiling of the booth, which in turn compromises the STC of these assemblies . To install an interior fan creates noise, and does nothing to bring in fresh air, as a small booth encloses very little air. To correctly duct in an air or HVAC supply and return from within a living room in an apartment could be a very difficult manuver, although not impossible. But damn near impossible if you can not attatch anything to anything within the room. Where would you get the conditioned air in the first place? The only place I can think of is connection to existing systems, OR some sort of unit in the window or mounted outdoors, but you must still duct the supply and or return to the booth. AND the ducts, and registers must be correctly sized, configured and installed so as not the generate noise themself, even for a simple fresh air supply fan. Not an easy task, as in a vocal booth, silence is the point, and if the booth is silent, but the HVAC or air supply is even slightly noisy, the mic will definitely hear it. In large rooms, the registers are usually located at a distance from the mics, so even small amounts of noise from them are usually negledgable.
Heat buildup. People give off heat very quickly in a small insulated space. A box of handiwipes is not an alternative for clients who are paying. HVAC is the key to this issue as well. If this is for yourself only, you are the only one to satisfy.
Construction noise. If you have neighbors who will complain of noise, how are you going to build without generating some.
Doors, jambs, and threshold seals. For any soundproof shell penetrated by ANY opening, the door assemblys create the most difficult challange to seal correctly. A haphazardly installed door assembly can lower the STC of a Rated enclosure by as much as 15 points. Even a properly installed assembly can still negate all other soundproofing assembly, if even 1/16th of an inch of space between jambs, studs are not caulked. Even with trim over the gaps, you MUST caulk. Joints in the sheetrock must also be caulked. The gap between the sheetrock and floor must be caulked before fastening a baseboard. All wall plates and stud to plate connections should also be caulked. And then you get to deal with the glass jamb assembly!!
Vibration isolation. That means decoupling the booth from the floor. Neoprene pads will work. But only if you install them correctly, and if they are "loaded" correctly. That means the right thickness and consistancy.(duro?)
I am not trying to rain on your parade, but the realitys of "soundproofing" are not as easy as some people think. That is IF real soundproofing is "the" critera you are trying to achieve. It is no different than building a small room within a room. Floating the structural floor of the booth takes up vertical space. The ceiling joists and assembly takes up vertical space. If you only have a nominal height of 8', you will soon be down to 7'. Add treatment, and you will even be lower. However. Like I said. Many people are happy with less. Like a frame and blankets. But thats not soundproofing. Some still call it a "vocal booth"

I call it a gobo., and thats not saying it is bad. Just not soundproof. I will try and post a set of drawings tomorrow if you still are interested. Other people may also post thier ideas too and or contradict my own. That is good. Helps clarify and solve brain farts

Anyway, I hope this illuminates some of the problems with real soundproofing. And doing it in apartment makes it even more difficult.
fitZ
