Thank You to all for an interesting discussion. The fact that no definitive answer is provided (or even possible yet!) regarding my original question just shows how much we have yet to learn. Again, I don't believe in singularities, anything infinitesimally small or dense, or one-solar-mass black holes (really?) because some things just don't pass the "there is logic in physics" test. Nevertheless, I'm sticking to my original point: the possibility that a very, very dense, i.e., large, neutron star would have the gravitational effect exhibited by a black hole, Fermi pressure or not. Anyway, this was fun!