Why not use GT2 en lieu of a Z-axis threaded rod or leadscrew?
A lead screw can be fitted with a anti-backlash nut to get past your concern about backlash. Generally, backlash is not that of a problem considering the weight of the carriage (e.g. Prusa), or whole bed (e.g. CoreXY or Ultimaker). Certainly if you're not using Z-hop, the Z screw will only advance in a single direction!

GT2 belts are always reinforced with fibres either glass, steel or some other fibre, all with their own (dis)advantages.

As far as I have learned is that lead screws are far better capable of transporting higher loads at the cost of speed. Also, a leadscrew will have more resistance so that if you unpower the steppers, the gantry will not plummet to the bed.