I wouldn't say it's a lamination looking at mine.
I don't think the setup is designed to tilt, just to be able to adjust coaxially, with the taper so the grub screws hold the shaft tight onto the body.


4th axis is well down my list. I've had an absolute hectic few months, and am only just getting the backlog cleared, which is why my touchprobe is still in it's box and not mounted ready to be used.