Joseph, If you look at the photo, the peaks are in line with the thread tips, the valley with the thread roots, so 180 degrees variation, in line with slight bend in the lead screw, exacerbated by the apron being fitted considerably out of line so the leadscrew was under tension from being moved sideways when the half nuts were clamped shut. With the leadscrew under tension, the slight bend in it varies the tension, which moves the carriage slightly as it varies, due to clearance in the gibs,, wear in the bed etc creating clearance.
With the halfnuts correctly aligned by having the apron correctly aligned by the method outlined earlier, the leadscrew is in its natural position with no tension on it, so a little bit of bend or runout in it does not move the carriage: the long thin leadscrew flexes enough to remain in line with the supporting halfnuts.