Adjust balloon callout dart's position

[wayfaringrob]

Per the discussion here, I'm looking for a way to adjust where the "dart" of a balloon callout hits the label. Currently, you can adjust the dart's width and where it points, but not the position of its junction with the label. It seems to choose between a left position and a right position, neither of which are suitable for fine-grain control over labeling within ArcGIS.