I don't know if this will work, I'm sure someone knows if this will work. Leave the drywall up, spray it with the thick, spreading foam that builders use for insulation in between walls. Then cover it with drywall or whatever you choose. Great thing about the foam, if you need to get into an area behind the foam, you just reach in and tear it out, when you are done with the repairs, spray foam into the area.
http://img.hgtvpro.com/HPRO/2005/01/10/hpro_best_bp08_spray_insul_e.jpg
http://img.hgtvpro.com/HPRO/2005/01/10/hpro_best_bp08_spray_insul_e.jpg