On the z-axis using a TR12x3, resolution will be 0.015mm at 1 microstep. This assumes no backlash, deflection of the carriage or issues with the table. If I'm out by a factor of 10, then the starting point would be 0.15mm. As the majority of any variation will arise as a result of deflection, the option to gear the z-axis is on hold.

The z and y axis are belt driven, the gear ratio is 2.8, so the starting point for mechanical resolution at 1 microstep is 0.1339mm. I will have issues with positional accuracy when cutting longer lengths, but I can compensate within Mach 3.

I'm guessing you started you build with better figures?