Wow this is really interesting. I need to think on this some more. I understand the spindle axis relative to x/y. And sweeping upwards you get the z tilt plus needle tilt in one orientation, and by measuring z tilt plus opposite needle tilt in the opposite orientation you can separate z tilt from needle tilt.
I also see you’re sweeping both sides of the feeler gauge, so in principle you could get needle taper and needle tilt and z tilt in different combinations and separate them back out with math. Although that seems a bit much so I am guessing you are aiming for lower noise by getting multiple points and averaging, and ensuring to start with that your needle is not tapered.
For a short needle your x/y resolution might be limited by steps per mm but if you have a long needle, say half your Z travel, you should be able to get a really precise measurement.