However I don't think you can completely eliminate backlash - some always exists otherwise the mechanism would bind up.
Ah well - you can and you can't.

You can:
Double opposing ball nuts and double AC bearings will give you zero backlash when properly adjusted - in the conventional practical sense. The key point here is that you must switch from sliding surfaces - which will bind or wear badly, to rolling contacts.

You can't:
Rolling contacts in the above rely on elasticity in the steel to work. Without some elasticity even ball races would not work. But having elasticity in the bearings means that when you have high enough loads there will be some movement, due at least to the elasticity. This could mean that a 50 kg load change could cause a 1 micrometre movement. Mind you, to call this 'backlash' is technically wrong: it is 'compliance'.

In practice: those with carefully engineered 'rigid' machines will happily expect repeatability below 5 microns. If you want anything better than that, you are going to need air conditioning, temperature stabilisation of the machine itself (eg water channels through the castings), some rather expensive rails (or air bearings), ball bearing leadscrews (of extreme accuracy), and seriously expensive metrology equipment (usually based on laser interference). This regime is where a factor of two improvement can mean a factor of 10 increase in the cost. Perhaps not needed for a hobby?

Cheers