The special tag is what prevents caravans from offering the metal (hence why it also appears on things like pattern welded metals). The problem is probably related to the hard-coded nature of the tag expecting there to be only one type of special metal (adamantine) so when reading the raws, the game, for the purpose of moods, keeps track of only one metal with that tag.
I'm not sure why it would be orichalcum, though. There are other metals which both appear before (adamantine) and after (pattern stuff) in inorganic_stone_mineral. Maybe related to the orichalcum bar appearing first in reaction_masterwork (as a rare result of batch smelting various metals), since this might be how the game realizes that orichalcum exists as a bar for metal moods? What happens if you move the adamantine wafer reaction to the top of reaction_masterwork? However, you also said that only weaponsmithing moods favor these special metals; it was my understanding that once adamantine is discovered, all moods favor its use in whatever form (though they may not overlap 100%; that is, it could be that adamantine can be used in some moods that orichalcum cannot be, though I doubt it). If that's the case I'm not sure why it would be limited specifically to weapon moods.