Damn, hope your hand is alright!
First, let me thank everybody for the awesome suggestions. I think I've buttoned up my plan for the next phase of the project, and more importantly, have added a new project to further improve things.
I'll compare cost of 2x2 strips of either pine or foam board. If it's close, I'll probably try the foam board. If it isn't (and I doubt it will be), I'll just use studs (probably make drywall installation easier, anyways). That'll give me a 2x6 cavity which should take r-19 relatively easy. I never would have thought air infiltration is as big a deal as it is, so I'll be sure to be meticulous with my vapor barrier and buy a few rolls of tape and spray foam.
What I didn't mention is that the siding (if you can call it that!) is hopefully coming off in the next year or two. As of now, it's this **** fiberboard stuff (can't be more than 3/4" thick) with the texture of lap siding on the outside. It comes in 4'x8' sheets, and is cheap as hell. That's literally all that is on the outside of the studs. In fact, mice have chewed through the bottom, and I can see daylight through the hole! When I spring for new siding, I'll look into some 3/4" or 1" sheathing and at least a 2" layer of foamboard on top of that. I'll likely due that all the way around the house, too. At least other parts of the house have some planking on the outside studs, but still no housewrap, and certainly nothing air tight. Hopefully that will go a long way towards improving things around here, and should be far more accessible than taking out interior walls!