The "galactic plane" is a man-made reference and not a physical thing. I don't know the accuracy of the determination in the canadian survey (your first link), but due to the size (thickness) of the galaxy and speed the solar system moves around it, there would be no noticeable year-to-year change in our position. The galaxy isn't like Saturn's rings, which are all on an extremely narrow plane.
Also, "the gravity of the plane" (from your first post) is meaningless. The earth is in orbit around the galaxy center of mass and passing through a region of higher density of stars (say...moving wrt the spiral arms....) doesn't change anything. Freefall is freefall.