Your formulae work for objects located at galactic center, then more the system is rimward more the location is shifted away from galactic plane.
Happy New Year too! Yes, I know the galaxy's orientation needs to be shifted because it's not fully face-on when seen from Earth. I also forsee that if you specify angles for right ascension and declination, but the distance is based on the galaxy distance of 3.83 x 108
parsecs, then you would be placing the stars on the surface of a sphere 3.83 x 108
parsecs in radius, so the distribution of stars will curve away from the plane of the galaxy at the rim. Given the vector from the Sun to the Star Wars galactic center, and another vector formed by the Sun and a star's RA and Dec angles, it should be possible to find the second vector's length at which it intersects the plane to which the first vector is normal, but I'd have to leave this to someone who knows more about vector algebra than me. This is why, instead of trying to programatically generate Space Engine systems for all 2000 stars in the atlas, I'd rather just add systems that were seen in the movies and adjust their distances from the Sun manually.