I thought, if I cleared a big enough space in the wall, that it would be possible to get a drill in there, and drill a hole diagonally from the cavity in the wall, towards the garage (away from the exterior). After clearing a hole in the sheetrock, and trying it out, it worked....
and if I was going to do it again I would just rip out all the drywall and put up fresh sheetrock. It would have saved both the electrician and the painter a ton of time and been cheaper in the long run.