Upstairs room too hot - can I install a room-to-room fan to blow hot air back into the high-ceiling living room?
It sounds like the living room is a very tall space.  It is normal for there to be significant thermal separation in such a tall room, befause heat wants to go up.  Tall rooms are a cultural indicator of wealth, which is one reason people like them; however the "wealth" part is that they cost more to heat. 

It can help to have some sort of fan stirring the air.   It does not need to be a breezy blasty fan, who wants that in the winter, right?  It just needs to stir the air enough to prevent stagnation.  We have a 34,000 square foot 30' ceiling building with 3 fans stirring the air, it doesn't take a lot and you don't really feel them.



As for balancing the vents, you don't need to hire a guy to work the little knob that closes the vent upstairs. You can do that yourself and just use trial/error - every time, bump it less distance than you did before, eventually you will settle on balanced.  If your vent does not have a knob, get one that does. 

Brace yourself for this: the vent setting that works in winter won't work in summer when the A/C is running.  You'll have to change it, probably opening upstairs 100% and partially closing downstairs vents.