Tonight, I remembered that the night before that Little Snitch was popping up requests to confirm a bunch of connections from named out to 0.0.0.0, among other things. In my delusional state, I hit something -- grant I think, but it might also have been deny. In any case, tonight I checked Little Snitch's list of rules by application, and didn't see named in there at all. On a hunch I went and killed the named process. I tried accessing a site by name and kblammo! It worked.
I'm not sure what went funny with Little Snitch, but something did. I still love the Little Snitch for protecting me from evil.