The plastic nuts on trapezoidal thread screws are the worst for wearing and play. What you can do is take the nut off and slit it crosswise in from the end. Then fit a hose clamp around the outside. This will allow you to compress the delrin nut around the thread, but don't make it too tight as you'll wear it quicker. A better longer term solution would be to make a new nut using some long nuts to suit the thread, and fit them inside a tube with a spring between them to put pressure on them, to help remove backlash. Sounds like hard work but it's really not.
cheers, Ian
It's rumoured that everytime someone buys a TB6560 based board, an engineer cries!