Hi Justin,
It isn't possible to manually move the key number list unless it has been converted to annotation. The list displays the same way as a dynamic label, so would be effected by a weighted area. So excluding those options it isn't possible to move the list away from the other labels with the set-up you have currently.
There is another possible solution to your problem, you could use a dynamic table within a layout instead of a key number list.
What is the final product you are aiming for? In what way are you sharing this map?
Regards,
Sam