Improve exception handling for background processes

There were a bunch of places where we fire off a process to happen in the
background, but don't have any exception handling on it - instead relying on
the unhandled error being logged when the relevent deferred gets
garbage-collected.

This is unsatisfactory for a number of reasons:
 - logging on garbage collection is best-effort and may happen some time after
   the error, if at all
 - it can be hard to figure out where the error actually happened.
 - it is logged as a scary CRITICAL error which (a) I always forget to grep for
   and (b) it's not really CRITICAL if a background process we don't care about
   fails.

So this is an attempt to add exception handling to everything we fire off into
the background.