As far as I was aware none of the ARR main scenario quests ever reward an Orchestrion Roll - some story dungeons do have Orchestrion Rolls (or at least a damaged one required to snyth an actual one) as a possible treasure chest loot, but that is not part of the actual quest rewards themself though (like the 2.4 main scenario quest dungeon Snowcloak has a chance of rewarding the Orchestrion Roll for it's theme The Warrens in the treasure chest dropped after Fenrir is defeated, but that is not connected to the story quest itself and thus requires you to actually run that dungeon to get, and even then it's not a guaranteed drop, although it does drop frequently).

Hence any Orchestrion Rolls that are potential rewards from dungeons required to be undertaken as part of the main scenario are not gained automatically when using the main story skip item. You'll have to run these dungeons yourself to get them I'm afraid.