Maplex tries to avoid overlapping leader lines, but it still does happen occasionally. You could convert to annotation and manually move the problem labels, but as you stated, you don't want to do that.

Are you using the maximum offset option? You may get better results with a smaller initial offset (say 5 points), but a large maximum (say 1000%). This will increase labeling time, however.

Maplex tries to avoid overlapping leader lines, but it still does happen occasionally. You could convert to annotation and manually move the problem labels, but as you stated, you don't want to do that.

Are you using the maximum offset option? You may get better results with a smaller initial offset (say 5 points), but a large maximum (say 1000%). This will give you labels with an offset between 5 and 50 points, but will greatly increase labeling time, however.