I am just getting underway with the costruction of my new screening room. I had intended to use 2x4s for the staggerd studs but two of the wall are 20's era construction with diagonal bracing and fireblocks (see photo) which preclude the standard staggered stud approach. Is there any reason not to use 2x2s for the staggered studs and just attach them to the face of the sill and plate centered between the existing studs? This would also make it easier to fill the wall with insulation.

2x2's are not strong enough and many will warp so badly they'll twist right off their nails or screws. I'd use 2x4s turned 90 degrees.

From the pic it looks like the blocks and bracing are flush with the studs which would mean your face mounted 2x2s would be in contact with them which might not give you the desired effect.

Yes, I thought about perhaps using sound isolation tape or pads of neoprene rubber between the 2x2s and the existing wall.

I second using and turning 2x4s. Padding between the walls sounds great, just be careful of materials as you don't want to develop any weird squeaks down the road.

I enjoyed the pic. They sure don't build them like they used to!