I would vote for the extra upstairs space, especially if all six beds are occupied. I know you did not ask, but the bathroom area makes me clautrophobic with all of the walls and little enclosed spaces. I think the bathrooms can be designed to feel more spacious yet still give privacy for 6 to use. Also, I would make the laundry area open to the hall. The two door entry from both bathrooms "wastes" wall space that could be used for a folding/sorting counter and takes space that could be better used by the bathrooms. This is all just my opinion, and I understand if the design works for you and your family.

The operation of these systems is somewhat counterintuitive. Contrary to popular belief during "Cooling" operation they do not make Cold...they remove heat and moisture. Proof of this is easy...place a thermometer at the return (incoming air) and one at the supply (outflowing air). In most homes you will have 74 deg interior air being pulled into the system and somewhere around 54 deg supply air being distributed to rooms. 20 deg was removed from the return air, along with moisture it contained. So in a case of "Hot Spots" the issue is often distribution if we know the system is sized (tonnage) properly for the home/space. In most home designs the supply air is directed at the Heat Load (exterior walls, windows, doors) and the flow of cooler air captures the heat (pure physics, heat seeks cold) and carries it to the nearest return vent where that heat is removed. In the description above it was said the only nearby returns are within the bedrooms. In a nutshell it does not sound to me like there is any airflow to/from your problem area. If it's a typical tall Foyer with a window at the peak then radiant heat is also being contributed. A reflective film can help. I hope this helps steer you in a good direction.

Generally, with so much light, you could go for the darkest gray on that same color chip as one of the adjoining rooms. It would stand up to the drama of the staircase and flooring, but I think you could up the ante with a dramatic/glam chandy there too.

Not beige means to me also not any of those yellow tones . I would look at grayed / greens for a neutral but I need to know what the colors are in the rest of the house