I dont believe the ball screws have errors. More likely it will be that they are not parallel to rails a bit.

Hence when i designed my machines and in general my practice is to align as much as i can one rail in all directions using straight edge and so on. Then next in same axis. Using mounted-bolted plate what makes me sure all the way they are parallel to each other. Then i mount the ball screws or whatever and move axis to one end. Tighten ball screw by hand , move another end, tighten by hand, then repeat that a couple of times till all is tightened. And as the ball screw was guided by the rail, that means they always have same travel and are perfectly parallel. So no Mach3 compensation is needed. In short i dont see any other way to do it properly, except if all is machined to fit, even then doing it so will be better and easier.

Same is valid for belts, where i make perfectly sure all possible is parallel and square.