Limit rotation in last IK bone

The purpose was, in fact to invite non-specialists to use the armature to pose the model:
https://www.z-anatomy.com/

Unfortunately, my mind refuses to accept that there is no way to get the thing to work properly:
keep the rotation limits in all positions, keep the controller following the objects that it controls.

In either way, it takes forever to get a full pose, if it even gets there. (starting from a supination anatomical position is not really helping with IK)
I guess that the only thing that I can do with it is to, as you said, prepare quietly a few poses, and make them available through the pose library.