Where is the return air vent? That can make a big difference in where the hot and cold air flows.

I see no reason for the upstairs hallway vent to even exist.

I believe the upstairs hall vent is there mainly an access to the main vertical vent that runs up from the basement. However, even closed, it does leak a lot of hot air through it. I should probably take some time to properly seal it up better.

The only cold air return is on the first floor in the living room, it is a sizable floor vent.

Ok, so the cold air return is in the right place for your goals.