I went and bought some red and white THHN write and a roll of electrical tape and a bag of wire nuts and opened up the light switch box yesterday, but quickly retreated.
I took a bunch of pictures and made a gallery of the inside of the box here
My main problem was lack of confidence and constrained space. I was hoping that the various connections would be easy to pull out and work with, but it looks like it will take some work getting them out from behind the far back panel, and with my large hands I might run into some trouble that I can't undo easily. I am also not well versed in how to use my little analog multimeter. Maybe I should get one of those simple no-touch live-wire testers? Are those recommended?
Any further suggestions on this job based on what the interior of the switch looks like? I figured that going at it from this end made more sense than rewiring each of the receptacles, since I now know there are at least 3 and possible 4 that are affected.