4 axis machining

Hello,
I'm a bit new to 4-axis machining and I've been machining features on axles. These axles were mounted on the A-axis. Fine.
But now I've clamped my ER32 collet block at 90° to the A-axis, with the nut facing upwards to secure my stock.
But I can't know his exact position until I lock it in the ER32 block because it moves downward when I tighten it. So I have to probe it.
I then need to use this measured value to set the part's origin in the CAD software to create the milling path. This is tedious and must be repeated every time I place a stock in the ER32 block.
Is there a way to avoid having to generate the program from the measured value?

I assume you can't just change the Z0 location as you need the Z/Y to be zero'ed with the 4th axis center of rotation.  Otherwise you could probe the top of the part stock and use "G10 L2 P1 Z0" to set a new Z0 offset.

If that's the case you can try putting a stock stop in your collet block.  The collet and nut will change Z-position when you tighten, but the part should remain (mostly) stationary... much like a lathe stock stop attached to the spindle (and not the collet).

Kind of a poor-man's dead-length collet system.

I think that this could probably be solved by using TCP kinematics. Then the probe positon could be fed into the kinematics (via a HAL pin).
If you expect this job to run for months and thousands of parts then it is probably worth considering. Otherwise the mechanical stop as suggested above is probably more expedient.

If you have a spare lathe compund slide (or similar) lying about you could mount the collet block on a slide, so that you can align the end of the work to a probe....