So before commenting your changes gazebo ( I don't even know what you will keep and what you will throw out ) I want to come back on the core.
What are the issues ? If you know what's the problem, we can find the right solution.
1 - I've already said it but authority is snowbally. If the AI or the player are able to "bash" Barbarian, you can get some good bonus.
2 - too many conditional, nothing upfront. Tradition and Progress gets a lot of Free bonus. They don't have to work on it. Free food, free production, free gold, free faith. To get food or production, you have to increase your culture output. But your only reliable way to increase your local culture is military tradition and it's one police later. So you have to rely on luck(@ barbarian spawn) because you can't settle new cities without infrastructure in the oldest or you will sunk into unhappiness pit.
3 - In higher difficulties, it's too much AI friendly and not fun for the player.
Free units, Free bonus, etc ... It's too easy for the AI to clean barbarian. It feels really unsatisfying for the player.
4 - You are the most terrain dependant. You can pick tradition anywhere :
On archipeledo, small continent, continent, fractal, or pangea.
Same for progress.
It's really hard to play authority on maps with too much water.
I think it's fine. But even on land maps, if you are in the middle of jungle or forest, hunting barbarian feel like a chore.
5 - It's the only police which I feel something is missing before getting 4/5 with .... you need to have 4 polices to make the combo works.
One side, there is no production/food and little culture.
The other, there is no science.
Progress is already rock and rolling with 2/5.
Conclusion : Authority is the most terrain dependant, is the most unreliable and the most conditional tree. Moreover it heavily favors AI over Human players in higher difficulties.