Welcome to Pond Boss, Jay!
I understand the desire to hide an ugly house. We have a junkyard of a property just across one of our property lines.
However, you do want to keep clearing trees and underbrush that are putting roots into your dam and/or putting leaves or needles into your pond.
I would consider planting some relatively faster-growing trees that do well in NC that you and your wife like for the appearance, wildlife habitat, etc. You can also have a lower visual border planting some nice bushes. (My wife likes it when I plant lilac bushes since they still thrive in our poor soils.)
If you get them established now, in a few years you will be able to clear out that fourth side as you see fit.
Good luck on your property and pond improvements!