Unfortunately having the Baron talk to other dwarfs wouldn't have the desired results. The desire is to not just make him angry, but to put him in his place. Think about it from a bar with an obnoxious drunk bothering you. Sure you could punch him in the face, and that would make him angry, but then he's just likely to punch back and being that he's drunk he might hit the wrong person. On the other hand if you outsmart a drunk you can make them feel foolish and angry but not know what to do with their anger. The best part in this case is it isn't that hard to outsmart a drunk and make them look foolish for you. They've done half the work for you already.
Correct me if I'm wrong but the Baron is going to make mandates no matter what, just with more mandates the more annoyed and stressed out he is. Or does it have to do with if all his "needs" are meant on if he is happy or not. It would be interesting to design a room that technically meets all his requirements, but actually just increases his stress levels as long as he is in it. For instance, he might want x, y, and z while making sure his room is at least super quality... so I suggest giving him a room that has x, y, and z at the lowest quality we can manage (might be hard with all the master craftsmen, but that can be fixed by having a non craftsman make the stuff. Then bump up the quality the rest of the way with caged rats. Sadly I don't know how hard it would be to cage rats, or how many rats you would need to make the room good enough.
Of course there are Dwarf laws that suggest that the dwarf that is appointed as Baron is an elected position, with the historical understanding that once a dwarf has been assigned such position that they maintain such position for the remainder of their life. In the past it has always been customary for the population of a fortress to arrange for the death of a pesky noble and replace them at their leisure, however that is by no means required for replacing nobles. One could say for instance simply fire the baron and appoint a new one. Nobles back in the Mountain Homes would not be able to argue with this as it is perfectly aloud by dwarf law. The logical person one might appoint would be Cog, but there is of course the added out of character annoyance with that, that anytime a stupid edict was made it would be Cog making it, and it becomes hard to explain why you are doing something stupid.
So anyways take some of this as random musings that Syntic might make to Cog, and anything that's ooc as just said in some way that makes IC sense.