There's some loose ends here because really we probably want to be
using the top-level server logger, and we should fix that, but in the
mean time, let's not swallow the errors as much, because the last
line printed doesn't actually show what the error was, but it could.
To do this, we distinguish between the current error (which might
be a wrapper around DeadlineExceeded) and a previous error which
we might prefer to return, if one exists, since it's more likely
the "real" cause.
