With the external return tube style, I reload through the tube ports. Make sure that not a single ball gets in the 'no ball zone' between the two return tubes, as when that errant ball comes up against the outside of either return tube, it will act like a sprag clutch and want to lock up the screw. This effect is pretty noticeable, and right away, too, so I'm sure you'd notice it. I think this is why it is impractical to try to load this type of ballnut from the end, because you would not be able to keep the balls out of the 'no ball zone'.
If the ballnut has a bit of wiggle to it, you may benefit from buying new balls that are a wee bit larger. If the ballnut freely spins its way down the ballscrew when oriented vertically, that is too loose. How loose? Hard to know, but preloaded ballnuts have a very smooth feel when rotated, but are not freewheeling when brand new.
Another possible source of backlash is the thrust bearing on the screw. Good quality thrust blocks use angular contact bearings, or even plain axial thrust ball or needle bearings so that backlash can be adjusted to a practical minimum. A lesser quality thrust block might be using ordinary deep groove ball bearings, which do not have a strictly defined path in the raceway, because of clearances. They can wedge and seem tight, but still not really locate the screw firmly enough for high accuracy applications.
Edit: any slop in your X or Y slideway gibs can also add mysterious lash to either axis. The slop in the X gib will show up as Y lash, and vice versa. It might not be backlash exactly, more like random position errors, with apparent overshoot or undershoot of true intended position.