For such a small travel unsupported rails will be better than supported since the latter has a lower force rating in one direction (sort of).

If the Z-axis is sufficiently heavy, i.e. the downwards force on the axis due to it's weight (so about 1.5*9.8=14.7N) and any frictionaly forces, then you wont have any backlash since the force will not change direction - gravity is effectively providing preload. If this force isn't sufficient you could just add mass to the slide, although clearly this will cause the acetal nut would wear faster which may or may not be significant. A nut sprung like you suggest can work well, I did that once with brass nuts on M12 rod a very long time ago.