Rule 4 of this group says :”04) Start your first post with an overview of your goals and where you are in the process... Research? Planning? Construction already underway? Finished, and wanna know why it doesn't work? ”. So here I am

Hey everyone! For the last few weeks I’ve been scouring the internet for reliable information on constructing my own small freestanding, room within a room, isolation booth to record voice over. and narration for audiobooks. And just likes all roads lead to Rome, I found myself here, reading through thread upon read for information. The noises I'd like to reduce are kids thumping on the floor above, sound of the AC unit when it's running (to help keep me cool), and db street noise filtering in through the cinderblock walls, window, and door.
I am in the research, planning, and purchasing phase. Half of the Green Glue I think I'll need was purchased at a discount locally, and I'm looking for deals on Facebook and Craigslist for whatever I can find!
Before I begin, here’s some groundwork: This is a rental house. I may be able to add or replace doors (though probably not), but I cannot change the drop tile ceiling, tear up the carpet, or add/remove the current framework and structure. Assembly and eventual disassembly has to make its way through a 32x80 archway.
The room I am hoping to build inside of is in the basement. It does not have a door because the room has no window. We are using it as our bedroom. It is carpeted (over cement) with a drop tile ceiling, and poorly fitting double doors that lead into a non-insulated closet that houses our well pump and water heater. The floor above the space I am hoping to build is partly carpeted, and partly vinyl flooring. As we have young kids, I am going to find out if the wife will let us put a rug in that area of the kitchen to cut down on thumps coming through (sound isolation begins outside the booth).
Problems: The room adjacent (with naught but an alcove separating, meaning NO DOOR), has 2 windows and an exterior door. We live next to a busy 4 lane road, on a hill.
With the portable AC unit on full blast, pumping cold air into the room, I think I’ll need to deal with around 50 dbs (an initial test, with more to come). With the AC off in the winter, probably around 36. In the winter I can plug the windows, which should help a little with road noise.
The road noise can be loud, infrequently. I haven’t been able to catch how many db’s the VW Golf’s without a muffler make in the basement, but it’s probably not louder than the AC unit going.
The exact dimensions of the space I have available is
54” wide
86.5” Long
87.5” Tall
So I am planning on building a structure that is
53” wide
85” long
86.5"
I am limited to these dimensions to the presence of a floorboard heater, and a 4 inch drop in the ceiling running through the middle of the room.
Design
From the outside in: 2 layers of 5/8’s drywall (with green glue between), attached to staggered 2x2 stud wall on a 2x4 bottom and top plate, filled with r13 or r15 fiberglass insulation, with 1 more layer of 5/8ths drywall for the inside. That will be for ceiling, and all walls. My calculations put that around 5 inches thick.
I chose 2x2s on a 2x4 bottom plate to allow for a staggered stud wall, the thickness of a regular wall because the max width I can have is 53". The only weight the wall needs to support is for the ceiling of the booth (and the wall itself).
Floor: from bottom up, sitting on the present carpet – 2x2’s 16 inches apart with aforementioned fiberglass insulation, 1/2 inch osb or plywood, with underlayment for vinyl flooring, topped with vinyl “click in” flooring. Total floor space I calculate somewhere a little less than 30 square feet. Depending on thickness of the walls, maybe even 23.
My hope is to keep the floor around 5 inches deep TOTAL, as I only have 86.5 inches to play with.
HVAC: Total volume of the space will be around 226 square feet.
Plan: Two externally mounted DIY silencer boxes for intake and exhaust, for fresh air, and pull in cool/warm air from bedroom. For the intake fan, I was thinking a 4 or 6 inch inline duct fan with 100% variable speed. Probably mounted to the East or South wall. I did see a design where both intake and exhaust were mounted on the door, but my plan is to try and get the intake down low, and the exhaust up high as opposite as I can with the limited wall space.
Door: 1 door on the south wall. My thought was, expose the “loudest” wall (the wall exposed to the other room with the doors and windows to outside) to a solid wall, but I may want to put a window on this wall also. Plan to use solid slab door, no holes, with push/pull, and an automatic door closer (but we’ll see).
Other problems: Doors are 80 inches tall, and I’d need another 2.5-3 inches to frame it and hang it. The entire wall, with drywall attached, can only be 86.5 inches tall.
Two solutions: A. Cut the door down to size (depends on what kind of door). This is probably the easiest if I use a slab door.
B. Make the wall with the door taller than the other walls, but leave enough space for the double layer of drywall.
Ceiling studs can't be staggered, so I guess I'll use 2x4's to keep the distance between drywalls the same as the walls. I know it's counter intuitive, but any thoughts on how to keep the ceiling "thin" and noise isolating? Or how to maximize the thickness to provide the best noise isolation?
Questions: Is this overkill for what I need? Should I skip the staggered walls? Skip a layer of 5/8ths? Use ½” on the inside?
Any worries about using 2x2’s for my walls, floor, and maybe ceiling?
Instead of building a window, can I use a door with a window already built into it? If so, should that be an exterior metal door (which is often NOT solid, but honeycombed), or do I try and find a solid wood door with a double pane window in it? If window on door is an option, I’d like to move the door from the South wall, to the East, to get natural light in from the adjacent room.
With such a small space, should I even worry about putting intake and exhaust fans across from each other?
The image "Sound Booth" is a mock up of what I'm thinking, as a top down view with some measurements, and notes about the surrounding space. The black lines represent the Sound Booth.
I don't have plans for electric or lights yet, but I thought I'd start with what I've got so far! My recording set up doesn't require electricity currently, but it'd be nice to have an outlet.
Please let me know if I forgot to mention anything!