What you are describing is the standard way to build a sound isolating wall. The staggering is not to create an airspace it is to physically separate the two wall surfaces so that vibrations are not transmitted via the wood frame from one gypsum board surface to the other.
An idea I had, but have not tested, is to put acoustic ceiling tiles facing inwards on the walls underneath the gypsum board. The theory behind this is that any sound that does penetrate into the wall cavity will be largely absorbed by these tiles rather than transmitting through the gypsum board.
I would imagine also lining the room, walls and ceiling, with the same tiles would help diminish the sound level also