I'll take another look at the codes to see if I need thicker than 15/32". It's a rather lightweight structure which but there is a second floor which is a small apartment.
In that case, I would definitely go with something more substantial. Having been through quite a few 6.x quakes, a handful of 7.x quakes, and a couple of 8.x quakes myself, I'm very much aware of just home much stress and movement this type of structure has to deal with. Your area hasn't been hit with quite such big ones yet, but they do keep on talking about "the big one" that is coming some day. I'd make sure that your place stands a goo chance of surviving that, by beefing it up decently while you have the opportunity.
I'm trying to do the work without hiring an engineer
You should probably reconsider that. Yes he will charge you money, but your life is on the line here. You might also find that your home-owners insurance policy will NOT cover any damage or injuries at all if you make unauthorized modifications to your place, and then it collapses in the next quake. That makes you personally liable for all damages and injuries, both civilly and probably criminally as well. It's really not worth putting yourself in that situation. Spend the few hundred bucks it will cost you to get the signed professional opinion of a qualified structural engineer. By all means do all the design yourself, but then call him in to check it, and make whatever modifications he recommends. It's cheap insurance! And it might also save your life, or the lives of your loved ones. I have personally seen what a quake can do to a structure that was not properly prepared for seismic loads: it's not a pretty sight.
Wall thickness:
stucco + sheathing = 2 1/2"
2x4 framing = 1.75"
furring and iso clip = 1 5/8"
2x 5/8" drywall = 1 1/4"
total:7 1/8"
So you are going with a single-framed wall with iso clips, instead of a double framed wall? That will work, yes, except that you do not need furring on the iso clips: you need hat channel. Sometimes people do call that "furring", yes, but more correctly it should he called "hat channel", for clarity and to avoid confusion.
Also, that will work provided that you only need moderate isolation: if you need high isolation, then you would need to make that into double-framed wall, in which case you skip the iso clips and hat channel: just put the second leaf drywall on one side of the second frame. Better still, put one layer of OSB on the frame, then a layer of drywall on top. Once again, that gives you much better sheer strength in the inner leaf, plus you then have a nailing surface around 100% of the room.
Good to know I don't need to be too concerned about right angles. I assumed it was to mitigate parallel walls which result in standing waves.
That's a myth.
Parallel walls do not create standing waves:
ALL walls create standing waves, parallel or not! Sometimes you do see incorrect advice on websites and forums about how it is necessary to "angle your walls to get rid of modes", but that is simply not true, and is a bad idea anyway. Its a basic misunderstanding of what modes actually are. In simple terms, a "room mode" is just a path that a sound wave can take around the room, then arrive back at it's starting point going the same way as it started, and in phase with itself. It's that simple. Modes occur in ALL rooms, not just ones with parallel walls. In fact, the worst possible modal problem you can create, is if you build your room as a sphere! A sphere has no parallel walls at all, but is sure as hell does have MAJOR modal problems, because ALL possible paths around the room are modes that occur a the exact same set of frequencies. The next worst is a cylindrical room, followed by a room with any concave shaped walls, then a cube, then a rectangular room with related dimensions, and finally the least problematic is a rectangular room with un-related dimensions.
Splaying your walls does not "get rid of" modes: it merely moves them to a different frequency, which will probably be higher than the original, since it will likely change the mode from being a single "axial" mode to being one or more "tangential" modes, which means it involves four walls instead of two, or it could even become one or more "oblique" mode, which involves all six walls (where "wall" includes "ceiling" and "floor").
It is impossible to get rid of modes by angling the walls. The ONLY way to get rid of the modes in your room, is to get a bull-dozer and destroy all the walls!

The only place you can mix in an environment that has no modes at all, is out in the middle of the countryside, with no trees, malls, or anything else around you for 60 feet in any direction, and sitting on top of a 60 foot ladder. There will be no modes that can affect you like that.
Modes (standing waves) are a consequence of having walls, plain and simple. If you have walls around you, then you have modes forming between them. regardless of the angles of the walls.
Some people look at all that, then think: "Cool! I know that low frequency modes are a problem, and that splaying my walls will push them to a higher frequency, so I'll splay all my walls and thus get rid of all of those pesky, bad, evil low frequency modes!". Wrong! Totally and completely wrong. The problem with the low frequency modal response of a small room is NOT that there are too many modes, but exactly the opposite: there are not enough modes!
It's a bit complicated to explain, but that's the truth
I wrote a long explanation about how all this works a while back. If you are interested, I'd be happy to dig it out again and put it here, in your thread. Let me know if you want that.
Splaying your walls can help with a totally different issue, absolutely unrelated to modes: flutter echo. But flutter echo can be dealt with using other methods, so it's not an issue.
If treatment can solve this then great.
In a reasonably large room, it is possible to damp the low end with a small amount of treatment, so that you get very smooth response, resulting in tight, clean bass and no artifacts. In smaller rooms, you can get close with stacks of treatment, but there are limits. In very small rooms, it isn't possible. The smaller the room is, the harder it is to treat, and the less likely it is that you will get fantastic results.
I live in a moderately dense neighborhood with minimal air traffic but significant street traffic 125' away. It's pretty quiet back there but neighbors talk and use power tools on occasion.
You should get out your sound level meter, and measure that. Use "C" weighting and "Slow" response. You need to know how loud that is, so you can design your isolation system accordingly.
More importantly is the isolation from footfall traffic from the apartment overhead. I don't have ceiling clearance to truly solve this issue but I was planning on doing hat channel, iso clips and double drywall with green glue for the ceiling as well.
That will certainly help, yes, but for impact noise like that, the very best treatment is to prevent it from happening! Just carpet the floor above. But down a good thick, soft underlay, and good thick carpet. Even if that is not your place, and not your responsibility, it is still very much worth your while to pay for it. The problem is that impact noise is structure-borne, and that's really hard to deal with. And really expensive! Much better (and cheaper) to simply kill it at the source.
Re: the control room, I was thinking of it more as a private space with a window looking into the recording area. Since podcasts/audiobooks are primarily headphone experiences, that would be the critical monitoring method. The control room in this instance would basically be for a producer so they could eat their lunch, tap away on their keyboard, have a private (quiet) phone conversation) and still be able to talk back and forth to talent as needed, all this while talent is reading for hours on end.
That sounds more like an office than a control room!
- Stuart -