What size are the ducts feeding into those rooms?
Unless the ducts are very leaky, the vent that terminates in the basement isn't doing much. If there is a return duct in the hallway and there's room underneath the closed doorway, some will go that route.
If you have any dampers on the supply ducts, you could try slightly closing the feed to the rooms that are hot and making sure those to the cold rooms are fully opened.
Having a common wall return duct will work somewhat, but not as effective as individual ones. It will also enable a passageway for sound from one room to the other.