The only downside I see is the 3D printer cheap leadscrews have a soft brass nut that might wear very quickly with the weight of a big tool on it, and they have a lot of slop that might affect your z dimensions. This cheap screws are design with light 3d printer gantries on them and only loaded in the direction of gravity. A cnc can experience loads opposite of this and you could have z variances of 1mm or more depending on bit selection, wear on the nut, material being cut. Think about a downcut through plastic. This might actually push the tool up, were regular bits pull the tool down.
I’m using this one on my prusa i3 http://www.ebay.com/itm/322101010139. The anti-backlash nut was much larger than any of the parts I found on thingiverse so I had to design my own but I’m pretty happy with them. 2mm per turn still gives me plenty of resolution.
Does the anti-backlash feature resolve the slop or backlash problems you described? What would be a suitable alternative to the brass anti-backlash nut?