This is a big-ish patch, but it's very straightforward.  Under this
clang warning, we're not actually allowed to have a global variable
without a previous extern declaration for it.  The cases where we
violated this rule fall into three roughly equal groups:
  * Stuff that should have been static.
  * Stuff that was global but where the extern was local to some
    other C file.
  * Stuff that was only global when built for the unit tests, that
    needed a conditional extern in the headers.

The first two were IMO genuine problems; the last is a wart of how
we build tests.