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.