The whole solar system sits perpendicular to the Galactic Plane. That’s why the Milky Way appears overhead.
There’s only one planet that rotates close to the Galactic Plane, and you have alluded to it.
I saw a show on the Science channel the other night which stated in 4 billion years the Milky .Way galaxy will collide with Andromeda.
Ouch, tilt indeed.