If everything else is working fine, then a quick improvement would be to make an anti-backlash nut assembly out of acetal. Make a couple of nuts with some kind of mechanism to close them together - on my first machine I used a couple of bolts with appropriate locknuts to pull the nuts together via clearance and tapped holes in the nuts. Not a perfect solution but something you could put together very easily. At a pinch, you can make a tap for acetal from an offcut of the leadscrew material - no need for hardening for that job. Probably a whole lot easier than trying to get backlash out of a rack and pinion setup - there's a reason why R&P tends to be used only on larger machines where leadscrews are too long for practicality. Looks easy but mechanically there are a few things that can bite you in the bum.