The proposed set up looks good for a backlash of around .015 -> .025mm if you get it right. Plenty good enough to remake the machine after the screws bed in and .025 mm start to hack you off, which it probably will

A stepper does 400 half steps per rev. A 5:4 belt reduction on to a 5mm screw would give you 0.01 mm per half step, add one microstep for .005 mm and it becomes credible. You could reduce it 5:2 and avoid the springy microstep but that could seriously affect your rapid at 36 volts.