That's my whole point - Experience and know-how will beat the crap out of money every time.

(sorry John, I didn't mean to come across like an ***hole. Thanks for expanding on that)
Yeah, I wasn't expecting it to be completely soundproof.
"Soundproof" is a relative concept. It may appear to be soundproof to a neighbor in a brick house 50 feet from an exterior wall, but listen at 5 feet. And thats the catch. A listener in an adjacent room may hear sound at a level that is annoying. For those who are designing spaces with SPECIFIED transmission loss to adjacent spaces, they must MEASURE the existing TL in order to design assemblies that will meet the specification. Usually, with an SPL meter, both inside and out. Of course, it takes a qualified user to analyse the results and extrapolate a solution for any given set of data, as frequency has a direct bearing...especially low frequencies.
One of my neighbors said she's never heard anything...which kind of doesn't make sense because it's pretty loud. and by "pretty loud" I mean "stuff moves"

Hahahahahahahahaha! I like it..."stuff moves"!
Thats a good one. I'll remember it.
Does her house have a brick exterior too? That might explain it. Since you were producing sound WItHIN a brick shiethed structure, and hers is too, well, that would be a pretty good indication why.
But in reality..you are absolutely right. Especially when it comes to structural transmission of impact noise...like drums.

You may not see it, but vibrations will transmit through connected structures very easily. Thats why "decoupling" is an important tool when designing for TL. In your case, the slab shouldn't be directly connected to the existing slab..nor should you use the existing exterior wall as part of the studio wall. It should be a seperate assembly..which basically means this add on room really isn't "added on"...as in building THREE walls that are connected to the house envelope. It should be an entirely seperate building, although it may appear to be an add on. The difficult part is the roof. Although, you can decouple the ceiling shiething from the roof via Resilant channel or other decoupling hardware.
Thats not to say you can't. It just means that if you use the existing exterior brick wall as the partition wall to the studio, you might have to design this wall in a different manner..like using Resiliant channel or something. In fact, you might consider building the rest of the three walls using a STAGGERED STUD design. This will help a lot. Especially if you plan on shiething the exterior with a brick veneer.
However, this all assumes you want the best TL you can afford.
Which btw brings up the issue of exterior shiething. Are you planning on matching the BRICK facade? Good for TL...but very expensive to impliment. I'd consider an alternative though with your budget. If no one can see the add on...who cares. Anyway, lots to discuss after I see your plan and pictures. Which reminds me. Take an exterior picture of the exact location where the door to the studio will be. Oh, an what type material is on the wall INSIDE...drywall or plaster?
One other thing. Before you design this whole wall in relationship to the studio...it might be wise to "open" the wall from the inside, where the door is going to be and see what type material is BEHIND the brick. If this is a fairly modern house, there should be some kind of sheithing that the brick is fastened to via mortar clips. If not..thats why you need to know.

I did a job remodeling a room with a brick fireplace facade one time. Just as we were finishing up the trim around the brick...we discovered the WHOLE BRICK FACADE was loose..we could move it back and forth over 1/2". In an earthquake, this would have collapsed

Anyway, later.
fitZ