My eyes lasered in on "distribution box" and I thought "uh-oh"....one of those triangle shaped things with one large flex duct going in and several smaller ones going out? If so, I'm not sure dampers will help here. The overall problem could be starvation of air due to bad duct design and layout. Start dampering down on the rooms that supposedly recieve too much air (but in reality may be getting barely just enough) and although the small bedroom may improve, the problem might just shift to other areas.
Not saying such is the case, since we haven't seen any photos of the ducts nor have the benefit of a site visit. Just wanted to put it out there as a possible snag.
Psychrometrics: the very foundation of HVAC. A comfort troubleshooter's best friend.