Hello,
Let me share my experience on this subject during the assembly of my printer.
_kaktus_, I agree with you that it is necessary to be very careful during the assembly of this axis.
The Z axis mechanism is quite simple, but in my opinion it hasn't been well engineered.
Depending on the actual geometry of the parts the system could become hyperstatic, or at least quite hard to move for the motors.
Each of the two half parts of the Z axis is composed by two elements: a guide rod and a screw/nut.
Each of these two elements has 3 joint points: one at each end and another that varies the position.
The 3 points of the guiding element are correctly defined and necessary to allow a smooth and accurate movement.
But the moving element would only need to have 2 joint points: the motor joint and the nut screw joint. The upper end joint is unnecessary and it could affect the function as it happens sometimes.
The motor flexible coupling is supposed to absorb the irregularities of the mechanism, but it can't.
This kind of aluminium elastic coupling can only accept some slight angular variations between axis, but not lateral variations like eccentricity.
In my case, I had to replace the original coupling by new ones I purchased because they were badly machined with a lot of eccentricity between their end holes. Even after that change, when trying to turn the screws by hand, it was quite hard, almost I couldn't.
So, I re-drilled the holes of the plastic upper guide for the screw, increasing the diameter by about 0,1 mm or so. Also a chamfer was made to each hole edge to improve assembling the screw rod and reduce the guiding length the created the blockage. I placed some light grease on that area.
During adjustement, it is necessary to sligthly untighten the bolts of the nut and the motor to allow them "float". Then put the nut close to the motor coupling and then tighten the motor bolts. Secondly move the X carriage upwards and try tightening the nut bolts and check the torque turning the couplings by hand. If it is still hard, repeat again to find the correct setting.
Put some light grease along the screw is advisable. However, after some time it would be necessary to clean it and replace as it will become thicker.
After that modification that improved a lot the smothness of the Z axis, I noticed that the left side screw was slightly hard to turn than the right one. I realized that the reason was the weight of the X axis stepper motor which is hanging outside the printer left side, seen from its front. That creates a higher friction on the left side nut/screw which is overloaded. I don't know if this would affect the behaviour of the Z axis, but I decided to introduce a modification to balance the loads.

- IMG_20190707_195144.jpg (163.63 KiB) Viewed 6464 times
I placed two straight bars of steel hanging by a string through a pulley, lift the motor upwards to counterload its weight.
The steel bars slide vertically and parellel to the rear side of the plastic main frame of the structure.
Now, turning the motor couplings by hand feels quite similar.
