Do you really want to keep it? If it is truly inedible, it will only ever be an ornamental tree.

I was hoping that taking care of it would "bring back" the quality of the fruit. However, as a new homeowner, I have no idea if the fruit was ever good.

Since the tree does provide privacy from the road, I would like to keep it.

Once the tree goes dormant for the winter, say around Jan., you can start taking a few branches out from the center to thin it out some. Taking 10% out shouldn't negatively effect the tree. Taking more is fine but understand you may cause the tree to put out few if any fruit next year or two, as it concentrates on putting out new leaves and branches.

If the apples are no good and there are several small trunks you could top work it next spring and add several different varieties of proven apples by using rind grafts and/or cleft grafts depending on the size of the trunks. With an established root mass the grafts should grow rather quickly.

Are you sure that it is an apple? When I hear "yellow, sour, inedible fruit, and looks like pear," I think Quince, not apple.