Deduplicate followup request handling.

This code's currently both gnarly and subtle; there's a lot of
nuance to the HTTP behavior, and a lot of state, but it isn't
obvious in the state of the objects doing the work.

Deduplicating work in HttpURLConnection with Job is a shy first
step. It also points out some potential problems with Job, where
we don't handle method changes or cookies correctly. That's
critical!