I was talking with Matthew Miller and we believe that we should change
the way our publishing process stages.  Specifically, we should have the
new CI job that does publishing push updates to both docs.stg.fp.o and
docs.fp.o at the same time.

Fedora infrastructure republishes docs.stg.fp.o approximately every 5
minutes and they republish docs.fp.o once per hour.  By pushing to both
we are creating a situation where accepted changes go live faster.  In
general we have time to catch any staging errors with a new publish, and
in the case where we miss it, the site is republished an hour later
anyway.