Rework the visibility computation algorithm in preparation
for distinguishing type vs. value visibility.

The changes to the visibility of explicit specializations
are intentional.  The change to the "ugly" test case is
a consequence of a sensible implementation, and I am happy
to argue that this is better behavior.  Other changes may
or may not be intended;  it is quite difficult to divine
intent from some of the code I altered.

I've left behind a comment which I hope explains the
philosophy behind visibility computation.