Green Glue is not a "magical converter of sound waves to energy". The process is called Acoustic Attenuation. It has a lot to do with the second and third laws of thermodynamics (or conservation of energy - not friction, which is a different physical process). Anything that absorbs sound (even the bricks, the sheet rock, whatever), converts sound into energy as matter absorbs them. Green Glue, applied properly, would be a significant aid in that sort of sound-proofing.
What the page on Green Glue was showing was a number of ways to help break up the sounds waves (and absorb them). Green Glue by itself wouldn't do the whole job and its efficiency would indeed be very dependent on how well it was installed - along the length of the wall and at a minimum thickness, I'm sure. Anything that will place a space between the two layers of sheet rock, that will absorb vibrations, will help with this as it allows the two layers of sheet rock to vibrate independently of each other and reduces the amount of "echo" the first layer transmits to the second. Through the wall ("His" side and "your" side, or front and back), the combination of "decoupling" the sheet rock from both sides of the wall was the first way, the space in between another (which could be filled with sound-absorbing foam, or even rock wool insulation [although rock wool settles over time and isn't really very good over long periods of time], etc), and what reinforced it even further was allowing the two pieces of sheet rock that were "Green Glued" together also let the energy of the sound vibrations to dissipate between the two sheet rock layers; each of the physical layers, with different properties, combined to reduce the noise significantly.
The problem with nails is not that they transmit sound into the sheet rock themselves, so much as that they compress the sheet rock against things that will transmit the sound into the sheet rock. The "decoupling" of the studs helps that, although the sound still transmits into the cavity between the layers of sheet rock and transmits the "open-air" vibrations into the studs themselves.
And someone mentioned the transmission of sound through the pipes, the floor, etc. That is very true, although a lot of vibration is absorbed the further the sound must travel through the floor (the "mass" the green glue folk were talking about) when talking about an apartment next door, and not above or below.
One other thing - I don't know that one layer of two pieces of sheet rock, separated from the wall (a must, even if it is with another layer of Green Glue-like material or foam, etc.) would be enough, although it would certainly reduce sound from what you have without a doubt. I don't know if gluing that layer to the wall would adhere correctly either, over any kind of long term.
Sorry I can't help with specific ideas on how to accomplish this without Green Glue, but something spongy that will also adhere to both surfaces would probably work better than what you have, being nothing.
I have a friend who is an acoustical engineer. He does a lot of sound work in BA from time to time, particularly for theaters and concerts. He doesn't live here, but I'll send him an email and ask if he has any ideas on how to absorb sound without losing space or using materials that are easily found here. One thing I've heard him talk about before is something as simple as heavy drapes in front of a wall. I don't know how practical that might be over the whole of the wall, or if it's even desirable or would be enough anyway.
Some 25 years ago or so, I was an engineering draftsman. I worked on precast concrete projects for NASA in Houston (a contractor to NASA on a few construction jobs) to develop walls for one of their lab buildings (I wasn't the engineer, but worked with him to design the actual system based on his calculations). They were explosion-proof (I don't remember up to what force) and sound-proof walls that were fabricated in our plant and shipped down to the NASA facilities and erected there. The walls we made were 10" thick, but "hollow" in the middle. The back and the face of the wall were each about 4" thick, with a 2" layer of a special styrofoam sandwiched in between them. The two faces of the wall couldn't touch or they would transmit vibrations. There was a bottom load-bearing lip the front wall sat on top of, made of neoprene rubber, which also insulted the sides and top (with a similar lip at the top) and allowed the two faces to actually move a little bit (a very little bit - minute fractions of an inch). We embedded hundreds of 1/16th inch thick hooked metal rods in both faces of the concrete (the rods weren't enough to transmit sufficient vibrations into successive layers of the concrete faces). The weight of the front wall face, when placed vertically, allowed the front face to move downward slightly under gravity and since they were connected by the small rods it also allowed the front face to compress the foam horizontally (as well as the neoprene below compress vertically) and made for a strong, sound-proof concrete wall. A bit more complicated than this simple description, but more or less correct. The joints between the erected walls themselves and the concrete floor were filled with a special rubbery foam.
I know this wasn't much help on the actual request from the OP, but I thought someone might take a little interest in the physics involved and an industrial-level application thereof