Z axis backlash adjustment help sieg x3

[replicapro]

I am converting the Sieg X3 and Im looking at the Z axis now and Im wondering if I should do one of the following:
1 fabricate an entire ball screw conversion
2. use the exsisting leadscrew head hardware and mount a ball screw to the exsiting head
3 leave it alone and just attach the servo

I dont know how to adjust the z axis backlash though as I can't see a adjustment screw
Here is the lead screw from under

this is on top

here is the amount of backlash

Looks to me like the head assembly has the lead screw as an insert to the cast iron head assembly holder.


What would you guys do here?