Just as a final comment, things are working very well at this point. A little bit of tweeking as suggested above helped.
But the biggest improvement was sparingly lubricating the lead screws. I had a can of spray silicon lubricant intended for the bearings and chain on my garage door. The can says the lube forms a dry lubricant layer that "doesn't attract dirt". I sprayed a bit of the lubricant into a plastic cup and used a Q-tip soaked in the liquid to apply the lube sparingly to the screws. That made a huge difference. After application turning the screws by hand was noticeably easier. And the chatter the anti-backlash nuts were making completely disappeared. All the axis run smooth as can be now.