I also suspect that it is not like there is a sharp division marking the "galactic plane". I suspect it is like the Earth's equator. Yes, there is a point where you are "on the equator", but the conditions 10 meters north or south of that line are not all that different - neither would ten million miles above or below the galactic plane. It is silly to say things like we are crossing the plane on 21 December 2012 at 17:03:47.592 UTC.

As far as gravity waves from the black hole at the center of the galaxy: I think they would propogate in many directions, not just in the plane of the galaxy, and so any influence they might have would have been felt on Earth for all of Earth's existence.

__________________
At night the stars put on a show for free (Carole King)