Script component source won't load when click "Edit Script..."
I stumbled across this blog post, which while the author didn't have the exact same problem as me, our issues seemed similar enough that his fix might work for me to. I downloaded the SSDT-BI 2012 package and installed it, and lo and behold, things work fine again. I'll just not even consider that somehow things worked fine for a year or more without downloading and installing SSDT-BI 2012, so I might be able to retain some portion of my sanity.