I picked up the backer rod a few days ago (2.3 cents per foot!!) and 30 sheets of 5/8" drywall arrived today. I've got two friends coming over tomorrow and we're going to start beefing up the outer leaf. I bought just one 850ml tube of Tremco Acoustical caulk to try it out before buying a case. If its just too awful to work with I'll have to figure out another option.
There have been two methods suggested around here for warming up the caulking (in order for it to shoot out more easily) - the microwave was one and soaking the tubes in warm water (wrapped in plastic of course) was the other. I'm not confident enough to put this stuff in our microwave and I'm worried about water leaking in and ruining the cardboard casing so I might try a third option. I'll be setting up a pretty large space heater while I'm working (since its currently the dead of winter) and I'm going to just keep the caulking close enough to it to do the trick (hopefully without it catching fire