How can I move hot air from a cathedral ceiling to colder bedrooms?
I suspect this will be a DIY project. 

Note that an alternative would be to simply install ceiling fans in the cathedral ceiling room to circulate its air better, removing most of the stratification you now experience.

(I've got upstairs/downstairs zones myself, with definite air exchange at the stairwell. I've considered installing a vertical tube with a boxer fan or two to get some counterflow there. Simpler alternative might simply to be to close the doors of the upstairs rooms, or to install a door at the landing, to limit the airflow.)