How to move hot air from a cathedral ceiling to colder bedrooms

There are a few things you can do which can help:

1) Adjust the dampers in the duct work. Partially close dampers in the ducts going to the first floor and fully open the ones to the second. Take some time to mark them so you know what goes where. It will probably take a few tries to get them set right. That's usually the first thing an HVAC guy will do for this situation.

2) Seal off the leaks in your duct work. Go around and find leaks and seal them with the aluminum backed tape. It's real sticky and has a peal off backing. Oddly enough, duct tape always seems to come loose on my duct work. Go figure. There are services which will come out and blow a smokey substance through your system to locate leaks and seal them.

3) This can be controversial, but you could cover your low returns in the summer and high returns in the winter. The theory is that this will pull more warm air out in the summer and more cold air out in the winter. There are magnetic covers you can get for this purpose like this:

But you may have better luck with stronger magnetic sheets and custom cut them yourself.

I'm not a fan of closing registers, but that's probably one of the simplest things to do.

There are systems that can be installed which will automatically adjust dampers in your duct work based on thermostats placed throughout the house, but they're pricey.

The room in question is fairly large and has several heat loss factors. Not withstanding the fact that the room sits on the cold basement floor, has large windows etc., the main problem is that the temp in the room is not thermostatically controlled properly. The only thermostat and heat zone is on the main floor and controls heat based on temps in the main living space. Your typically closed bedrooms and lower level rooms will never heat or cool at the same temps as the room the thermostat is monitoring. If you really want to have accurate temp control, it may be necessary to install zones. One zone for open living areas (kitchen, dining, living spaces) , a zone for bedrooms, and a separate zone for the office level. Without separate zones, you cannot monitor and adjust temps in the areas isolated from the living space.