So, it turns out the "live" wire is carrying residual voltage from something (I'm guessing a bad switch) and my tester was picking it up. I discovered it was actually not live when I inadvertently touched it while removing the ground wire nuts at the location on the right. Here, I've got all 3 locations pulled out and ready to patch the drywall. I'm thinking I'm going to lose the light at the end of the hall and turn it into an outlet since there are no outlets in this space. I'll need to get into the crawl space and run another wire for that.