Reminds me a little of one of the governments in Civ 2, all those years ago ... Fundamentalism. It was outstanding for warmongering, at a penalty of reduced scientific development. That limit could be worked around in Civ 2 by having a really, really large empire.
In Civ 3, I've read many accounts of players who largely turn off research after Military Tradition to get Cavalry. If a new Fundamentalism government were made available at the start of the Industrial Age, say, Monotheism (Middle Ages) and Nationalism (Industrial Age), a warmonger might choose it instead of Fascism and stay in it while going for Domination or Conquest.
Yes. I added Fundamentalism at Monotheism (50% max tech, rampant corruption, Forced Resettlement but zero unit support). The AI only very rarely selects it, which I'm happy with. I think it is an okay option if you find yourself either in a dominant tech position or needing a desperate last roll of the dice to eat into a strong, demilitarised neighbour.
On the wider topic, after much unsuccessful testing I did a u-turn. Rather than nerf Republic, I've created later Republic alternative options that made Republic less attractive by comparison (particularly now that I've softened Anarchy considerably, increasing willingness to go for an extra revolution). Combine this with the later appearance of Republic and the earlier appearance of Feudalism and Republic gets considerably less exposure in the game, but is still one of the dominant government types. My variations on Republic are:
(Navigation) - higher worker rate and slightly better unit support than Republic, but Xenophobic.
(Corporation (think countries with a degree of Democracy but limited independent judiciary or media)) - significantly better unit support and military police than Republic, but higher corruption.
The AI is incredibly sensitive to any unit support changes to Fascism and Communism and seems to switch to only ever doing one of those governments in a given game based on the most minimal of tweaks. What I particularly like is that the AI seems to use my Imperialism and Plutocracy as staging posts to build up a military before deciding whether to revert to Democracy / Republic or to go aggresive and select Fascism, Fundamentalism or Communism. My perspective is that selecting favoured AI government types doesn't seem to have much effect, although selecting a shunned government does seem to have a big impact.
After much testing (I love watching those AI guys strut their stuff) I had a couple of test runs in a row where every Govt, new and old, featured in an AI only playthrough (Fundamentalism and Plutocracy very rare, Imperialism as popular as Republic). Happy enough with my solution here, but totally floundering on difficulty settings - so I think I've just got a little lucky rather than showing any sort of command of the editor!