Need help with setting z-offset on Klipper for my S1 Pro - eviltoast

I’m getting increasingly frustrated trying to get my printer calibrated. I’ve done a bed calibration using screws_tilt_calculate, and that’s all nice and good. Got a bed mesh variance of 0.19mm which seems great.

Now for the z-offset, it won’t let me get the nozzle low enough. No matter how low I set the Z minimum, it won’t let me get closer than about 0.5mm to the bed. I’ve tried setting the position_min in [stepper_z] anywhere from 0 to -9 and I get the same result every time.

If I raise the bed, the probe adjust its height accordingly, so the result is the same.

What can I do to fix this?