Backlash should not be an issue, particularly while using a dro, as long as you are not trying to climb-mill. That is unless the backlash is so much that failure of the nut is imminent.
As well as Andrew’s point, the difference between mid point travel and the extremes would be a useful piece of information. It would indicate whether the wear is just the feed screw nut or the screw as well. Little point, or short-term repair, of fitting a new nut to a badly worn screw.
It would be good to know that acetal can resist climb-milling forces when used for a mill feed screw nut. I have my doubts on this but would love to be proved wrong. Lathe feed screws are generally a different ball game in this respect.