The spline shaft is bent. I have replaced a number of these over the years with the exact same symptoms.
How is your placement? Your 180 degree placements should be skewed if the shaft is bent. 0 Degree placements are typically acceptable due to minor theta adjustments after vision.
I believe the part you are looking for is PPH-0500 from Fuji.
Head #1 Q and Z Calibrations are required after replacing.
I always recalibrate the camera position, nozzle position and camera resolution when I replace the shaft. Better to start fresh with known good calibrations.
I have witnessed operators open the MFU Safety door while the machine was picking parts and proceed to move the head out of the way by grabbing the shaft. I tend to believe this is the root cause of most IP 3 Z shaft damage.
By the way , changing the ball screw will also sort your problem out because you will have to carry out the Z-axis setup ( belt tension etc ) as part of the change. so it is worth a shot to carry out the setup and see how it goes! you will have nothing to loose...