I have a RF-31 round column, but as far as the Z goes, they look very similar.
In my case, I removed the micro feed hand wheel and replaced it with a timing pulley. This is driven by a servo and in my case, I used a 2:1 ratio. I also found that by loosening the two screws that hold the pinon case on the side (part # 143 on page 16 of the manual) and tapping the whole housing towards the front, I eliminated most all of the backlash. Yes, there is still some, but not enough to give me problems. I also removed that stupid spring on the other side and used a counterbalance to give a higher pulling effect.