The original design could accommodate a slightly modified anti-backlash nut but in the wrong orientation (wrong orientation has the spring supporting the weight of the gantry). This is simply mirrors that part for the correct orientation of an anti-backlash nut. This correct orientation has the spring helping gravity push the gantry down.
This is the nut I used (Affiliate Link https://amzn.to/3UbgINB ) a round mounting surface delrin T8x8 anti-backlash nut.
The hardware specified by LMaker is fine BUT should be installed with the head of the button head cap screw on the spring side of the nut. Install the screws before the spring so the spring slightly rests against the edges of the screw heads once the spring and the slave nut are installed.)
If you still want to use the original model, due to space constraints the slave nut (the smaller one) needs it's diameter reduced to fit. I had to chuck my nut in a drill and used a utility knife to scrape away about .5mm from radius while spinning the nut like in a lathe.
The author remixed this model.
Mirror model