If the table is level, and the spindle does not tram in square, then you need to shim the spindle cartridge, assuming that you can do this on your machine. Much as I didn't believe at first that this was necessary, when I rebuilt my Haas, I was very careful to sweep the table and shim in such a way as to get 3 point support (approximately equal spaces between shims or to the unshimmed contact point) around the flange of the spindle cartridge. Once I had the shims figured out, I put a light smear of loctite around the flange face, and then tightened it up. That was supposed to 'bed' the spindle to improve its bearing against the head casting. Maybe overkill, but then I frequently do that whenever I tinker with my toys.
I also am of the opinion that a quite light finish cut is needed to prevent the tool flexure effect from tipping the tool tip out of the level plane.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)