I have a feeling that, relative to the centre of the milky way, we have barely moved over the course of many ice ages.
And if I'm not mistaken, didn't the term singularity just evolve into black hole, as in singularities ARE black holes...well, at least the center of the blackhole is. The black hole itself is caused by the event horizon around the infinitely dense center.
That's why I'm confused people would think a singularity is a "baby" black hole.