Ted, ecobatts are fiberglass insulation, just anothef brand than pink.
If you use R21HD ecobatts in staggered wall you can achieve R21 in the voids between the 2x4s. Where there is a 2x4, you do not compress the R21HD: you cut it to fit the gap. That might pass inspection. Check with your inspector. Report if you can.
If you go double 2x4 stud wall with the 1" air gap (total thickness 8" not including covering Sheetrock), you can get R30 just by using R15HD ecobatts to fill the void between the 2x4s. Add to that the R value of the 1" air gap and of the Sheetrock (?) and you should get both superior thermal and sound insulation though at a possibly higher price.
I know the recommendation usually is to go with the pink stuff but I am not sure it comes in High Density format, which Knauf rates at higher R values than non HD. Another advantage of ecobatts IMHO is that they are a more sustainable choice and a possible way to achieve higher air quality (no formaldehyde). This might matter to you as the double door entry to the theater recommended with double stud walls will provide an air gap too where the air quality may depend on that between the double studs in the wall. That is assuming there is no flexible seal between the two door frames isolating them from the 1" thick air envelope sandwiched in the double stud walls. I hope to be clear but realize I may not be.
On that topic I would appreciate if e.g. Ted could clarify what is recommended to seal the gap between the two door frames that prevents noise transmission: GOM, vinyl, any other flexible material? Hope I am not over thinking it