To get back to topic, I've always though a "Corpratism" model would be most flexible.
From Wikipedia
Corporatism is a system of economic, political, and social organization where corporate groups such as business, ethnic, farmer, labor, military, patronage, or religious groups are joined together into a single governing body in which the different groups are mandated to negotiate with each other to establish policies in the interest of the multiple groups within the body.
In essence I'm saying their should be a multitude of independent 'power structures' co-existing and all 'pulling the strings' at the same time. This is essentially what we already have with the 'royals' and the elected mayor all making demands at the same time, we just need to have the currently pointless demands made more purposefull in nature (which everyone agrees on already) and make the power groups making the demands do some 'negotiating' so were not spammed with constant demands, instead we get a more meaningful consensus demand which is actually something the fort NEEDS. After all the idea of 'government' in a god game ware the player actually controls everything can only boil down to "who gets to make the impotent demands".
Naturally the player can control which structures flourish (by meeting the start conditions) and which don't (lever) but the normal course of events would be multiple structures running concurrently and a power-sharing arrangement among them. This is also a rather accurate representation of medieval society and particularly Dwarven society as it's usually portrayed.
Major power structures and what they want to obtain
King: Kings in DF should be more explicitly hereditary with crown-princes and the like. The King seeks to keep himself from being deposed by the nobels.
Nobels: Dukes and Barons shouldn't just be stepping stones to the king but exist in limited numbers permanently, average dwarves might become Nobels by accuiring wealth or fame. Nobels want to usurp the King.
Church: When religion is improved the various Pantheons will have Clerics and all the clerics will together form a kind of Holy council. The church desires grand constructions and occasional holy wars.
Mayor: Chosen by popular vote the mayor represents democratic inclinations, he seeks to keep the population happy and himself re-elected.
Guilds: Profession group based Guilds have a guild leader and are chosen by skill in their profession. Guilds seek more work for their Guild members and to keep profession skills to a narrow group of highly skilled group members. The Guilds act independently and each one can be considered a power center in and of itself.
Clans: Family relationships give rise to clans and the oldest member of each clan is its Matriarch/Patriarch, all the clan leaders form a group called the Clan Elders. The Elders seek population expansion and domestic living space expansion.
Military: The Champion will be a singular position in the next version and would be a logical representative for the desires of the military dwarves (or perhaps the Captain of the Guard instead). The Champion wants arms, equipment and defenses to be built.
Merchants: Dwarves operate shops would form what amounts to a merchants guild (but perhaps called something else like "Syndicate" to distinguish it from the Profession based guilds), Merchants seek more trade both internal and external.
Other possible power sources: Magic users (if not represented by a guild), Scholars/Lore masters (again if not in a Guild), Adventurers & Foreigners (if such things are allowed to live in the fort)