I am sure you already know that the air going upstairs will end up downstairs.
Any way to damper the whole upstairs at one spot? I have a damper right above the furnace that splits the house in half.
Some air will come downstairs, but certainly not all of it. A lot of it just gets wasted in the crawlspace where the ducts are, and a lot of the "coldness" gets absorbed by all the stuff upstairs.
The upstairs is just two rooms with a bathroom and a tiny "hallway" in the middle. There is only one vertical duct going upstairs which splits into two for the two bedrooms (plus a small branch off to the bathroom). That vertical duct happens to run through a coat closet on the first floor so it would be very easy to access to put something in there.
Now that I think of it, there might actually be some kind of damper down in the basement. Remind me to check when I get home.