I completed my theater room addition (on the 2nd story) last year and used the same double wall construction method you are using. I did use two layers of mass loaded vinyl on the floor but not in the walls. I separated my double walls by about two inches with double 5/8 drywall on each side with Green glue between the drywall. This makes for a tremendous sound barrier. Really amazing. At reference levels you can hear some sound but it is incredible the damping and sound reduction that is present in my house. It is so good that my wife and I can watch a movie at normal but not reference level and the kids can be playing or watching another movie in the game room next door with no problem.
Not sure what the effect of the mass loaded vinyl in the walls would be. I would space out my walls a bit farther vs trying to use the mass loaded vinyl. I have also used the mass loaded vinyl in an outdoor fence project and it is not easy to work with (due to the weight). Make sure that you seal under the drywall with the acoustic sealant that the Green Glue manufacturer makes.
The weak link for sound passage in my room is the door even though we customized a solid wood external door with mass loaded vinyl and additional wood. A double door system is best.
Procella P8 LCR, Procella P5V for Atmos speakers
2.39:1 Seymour XD, 116" wide & JVC 4910 projector
Parasound Halo A31, Parasound Zonemaster 1250
JTR Captivator S2 (1st to receive New 2017 version) and Dual Seaton Submersive HP+ up front, Dual JL Audio F112 in the rear