How to run HVAC vent into cold room, below a supporting beam?
If the addition that you mention has 3 side walls and a ceiling, heating and cooling this room from the same furnace as the rest of the house is nearly impossible. The 4 surfaces exposed to the weather will loose heat in the winter and gain heat in the summer at a faster rate than the rest of the house. If this is the way the addition was built, then a separate heating and cooling unit or the existing system should have been zoned to provide it's own temperature control. Adding too much air supply will cause large temperature swings in the addition. As far as giving advice on running the duct, I would have to be there to see the actual space and items you mention. And "no" I would not use plaster board for a duct. At this point, I would add it's own heat/cool system or better yet have a professional in your area give their advice.