Anyone a suggestion how to get the greys more neutral?
1) Are we talking about inkjet process? Or Silver Halide? Or solvent?
2) What measurement mode are you selecting after your finish measuring the target? M0 and M2 will change the gray axis ever so slightly, with M2 often being a little warmer. M0 is the default.
3) What rendering intent are you printing with?
4) What lights are you viewing prints under? Is metamerism at play? Have you viewed under daylight?
5) How are you determining gray axis neutrality?
If you're printing with Perceptual, you'll get a perceptual gray axis that's relative to the paper white color. So you'll see a cooler gray axis on bright white papers and a warmer gray axis on natural white papers. This is normal and what's needed for the tonality to look right.
One last suggestion is to choose a patch count that has a bunch of gray patches. In the Patch Set module you can increase the patch count by one and see the number of gray patches increase. Repeat this process until it suddenly hits a combination with much fewer gray patches. Use a patch count value just before this point that maximizes the number of gray patches. This won't help the 'problem' you're having, but its a good policy and helps optimize the gray axis.