@SignPostMan a plane is defined by 3 points. 4 points make it overconstrained. Bed leveling will try to even out any deviations, but that simply isn't possible when the interfaces aren't mounted to the z axis. The only thing I can imagine is that you'd have the leveling algorithm only take 3 points into account, and then calculate where to move the 4th axis, just for additional support. I don't think the firmware is currently capable of doing that.
What is your purpose for the 4th axis? Why not follow the ratrig/hevort triple z setup?
Small side note; you have to make sure the 'leadscrew coordinates' are actually the coordinates of the center of the balls that support the bed, otherwise the calculation will be off even more.