Cost to convert 2x4 exterior wall to staggered wall

Hello, I'm new member to the forum I'm in the design phase of my music studio/theatre room. I have a room where the exterior wall is a 2x4 with stucco on outside, and with 2 windows.

My plan was to rip out the interior drywalls, add a 2x2 top & bottom plate and use staggered wall on it. The wall dimension is 20'x8' with 2 windows. My designer tried to talk me out of it and told me it'll cost me 10k to rip it out and do staggered walls, does it sound right? it's much more expensive than I thought.

He told me to simply build a wall on top of it without removing the dry wall, which of makes it "triple leaf" that I don't want.

He told me by removing the drywalls, I would damage the the vapor barrier, and redoing the vapor barrier + add more insulation will cost me.

My question is:
- Is this true? Is what I'm doing uneconomical?
- If I were to convert my 2x4 exterior wall with staggered stud config, do I actually need to rework the vapor barrier/insulation?
- When converting 2x4 wall to staggered, do I actually need to add more insulation to fill the extra 2" gap? or can I simply leave it?

Thanks for your suggestions!

Desperately needing your ideas

Kelvin

PS - My original plan was to convert it to staggered wall, with 2 layers of drywall with green glue applied. I'll add an interior windows using product similar to soundproofed windows.

Thanks for all the suggestions! I've got this ballpark figure with safety margin built:

wood framing: $12/sq.ft (labour only)
materials: $6/sq.ft (delivery is extra; assuming only the interior side)
drywall: $8/sq.ft (material+labour)

I think that's how he came up with the estimates. He's probably assuming the $8/sq.ft include double layer & GG

I'm still debating whether i'm overdoing this by decoupling the exterior wall. Or I could simply add a layer of drywall with GG, and add the interior windows.

Anyways, thanks all!

Thanks for your suggestion, Dennis.

Basically, I live in a townhouse and my plan to to knock down the partition wall of 2 rooms, create a bigger multi-purpose room (for moderate sound level band rehearsal & for movie/entertainment). room ~20'x16'x8'

I want to reduce sound leakage to outside and to my immediate neighbors. I want to do some music recording too.

The current room has:
exterior wall: stucco on stucco wire, R20 batt, 2x4-16", vapor barrier,1/2" drywall inside
party wall: double wall, 1" air gap, acoustic batt, acoustic caulked, 5/8" drywall + 1/2" sound deadening board on both side
interior wall: uninsulated 2x4 typical wall
floor: wood subfloor, no insulation, glued/nailed drywall
ceiling: single drywall.. above it is R40 insulated attic

My ideal plan is:
- add 1 layer of 1/2" or 5/8" drywall with Green Glue (GG) on the party walls, and on the ceiling
- Ripped the interior drywall of the exterior wall, extend the top & bottom plate and create a staggered wall. use 2 layers of drywall with GG
- Create a staggered wall , insulated for interior wall
- add a owens corning quiet floor pad, and add 2 layers of plywood with GG.. - Use linoleum tiles for the flooring
- add 2 interior windows

My budget is $17500. At most $20000. This includes new lighting & switches

My problem is.. i dunno if i'm overdoing by ripping out the drywall of the exterior wall and extending it using staggered configuration.

I *think* it's neccessary though.