I've run into this before when generating a series of Exhibit Maps based on parcel shapes. While I am not aware of any methods available to avoid Graphic Layout Elements from overlapping with specific features, I have used a workaround to the same effect.
Typically, I follow these steps:
- Make a duplicate of the feature class (or optionally, the selection set from it).
- Set Data Driven Pages to use this new feature class instead of your old one.
- Set the symbology for the new feature class to completely transparent. (or you can wait til you're ready to export the map series to do this).
- I would advise you add a Scale column to the new feature class. You
can set Data Driven Pages to use the scale listed for the given
record, which will help better position your data-driven feature on
the page.
- Manually adjust the transparent shapes as needed to nudge the center of the actual shape away from your dynamic text box. This will involve reshaping the feature so that its extent goes opposite of the direction you want to nudge it. If you want the shape to move to the left, reshape the transparent feature so that it gets bigger to the right.