Nice idea, but I don't like some of your adaptations. Philosophical/Creative would be too powerful. Let me try! Though, note that they may not be quite moddable.
Aggressive:
-small chance for a double damage in a first stack.
-Combat I free promotion
-Cheap barracks.
-Free units maintenance (based on number of your cities).
My reasoning: I like Aggressive as it is. We are exchanging a Drydock for a nice thing that spices the game - the chance is not gamebreaking, but it can give an advantage.
Creative:
-+1 culture in every city.
-Theatre gives a small chance of an extra population point after the city grows to the next level. (that is, if you hop from 5->6, you can find yourself immediately on level 7)
-less War Weariness.
-Golden Age makes people happier.
-Cheap theatre, cheap colosseums.
My reasoning: Another not gamebreaking bonus - we get some nice things nerfing the initial bonus (just like free monument). I like Creative as it is. Why theatres give more pop? Well, the glory of their awesome plays are attracting people! And most people don't like Creative - THAT will let them like.
Less war weariness and GA happiness comes from a legend, that after Persians conquered Athens, people didn't even react, because they were busy watching Olympics. Persians were confused even more after they discovered how much worth is the prize of... how do we call the ancient olympic thing that winners get? I can't find the word for it.
Charismatic:
-+1 First Strike for every unit.
-free Great General.
-+1
Happiness.
My reasoning: Remember Heroes of Might & Magic and the morale bonus, that your units sometimes could get? Well, you understand the First Strike. The free Great General comes from the simple fact - often leaders were leading their armies themselves. We could reflect that with GG. (and would make promoting your starting Warrior to City Raider III to a... nice rushing fun.
) And happiness is happiness.
Expansive:
-+2 health.
-gives the central tile +1 food per 7 population points.
-+25% normal buildings speed.
-cheap Granaries.
My reasoning: At the cost of Harbors, we get a little enhanced Expansive. +25% normal buildings speed - well, some civilizations were really adaptive to what surrounded them. And I still remember the quote from "Asterix & Obelix", when Obelix said, after waking up in Rome (praetorians caught them sleeping on the wasteland and transported into Rome): "Whew! These Romans are building awful fast..."
(it's a loose translation, of course) And the central tile is a little nice bonus.
Financial:
--50% corporations maintenance cost.
-faster scientific process.
-can rushbuy whenever he pleases (no need for US)
-free tech from the start of each era.
My reasoning: It's something from Scrooge McDuck, and something from Civ3 Scientific, changing Financial into a late gamer. It gives you this - you settle a city, pump cash, and you can make infrastructure quickly!
Industrious:
-+50% to building wonders.
-Engineers give +4 production.
-Double speed to Forge.
My reasoning: I like Industrious as it is. And as some traits have been pumped, this one needed it too.
Imperialistic:
-+50% to Settler production.
-+25% to Military production.
-+100% to Generals.
My reasoning: All the imperialistic empires were military powerhouses. Rome, for example. It seems fit.
Protective:
-+20% to defense (just defense).
-Archery and Gunpowder units get Drill I, City Garrison I.
-cheap walls and castles.
My reasoning: The defense gives you big bonus to a weak trait. You can escort siege units with archers and longbowmen better. You can escort pillagers (they are vulnerable to an attack usually, until Knights and Cavalries). And the rest is the same.
Philosophical:
leave it as it is.
Organized:
--50% civic upkeep cost.
-cheap courthouses.
-workers are working twice as fast.
My reasoning: That's a boost that is... organized. It gives an advantage, but not as awesome as in Civ3. You lay fast roads, you lay more cottages, you cut jungle in just two turns. Now everything is not as long-taking as in Civ3.
Spiritual:
-No Anarchy.
-Cheap religious buildings.
-Monasteries never obsolete.
-100% chance to spread religion.
-+1 happiness from Monument, Temple, state religion, and wonders.
My reasoning: To space an already good trait. (Heck, every trait is good)
Aggressive:
-small chance for a double damage in a first stack.
-Combat I free promotion
-Cheap barracks.
-Free units maintenance (based on number of your cities).
My reasoning: I like Aggressive as it is. We are exchanging a Drydock for a nice thing that spices the game - the chance is not gamebreaking, but it can give an advantage.
Creative:
-+1 culture in every city.
-Theatre gives a small chance of an extra population point after the city grows to the next level. (that is, if you hop from 5->6, you can find yourself immediately on level 7)
-less War Weariness.
-Golden Age makes people happier.
-Cheap theatre, cheap colosseums.
My reasoning: Another not gamebreaking bonus - we get some nice things nerfing the initial bonus (just like free monument). I like Creative as it is. Why theatres give more pop? Well, the glory of their awesome plays are attracting people! And most people don't like Creative - THAT will let them like.

Charismatic:
-+1 First Strike for every unit.
-free Great General.
-+1

My reasoning: Remember Heroes of Might & Magic and the morale bonus, that your units sometimes could get? Well, you understand the First Strike. The free Great General comes from the simple fact - often leaders were leading their armies themselves. We could reflect that with GG. (and would make promoting your starting Warrior to City Raider III to a... nice rushing fun.

Expansive:
-+2 health.
-gives the central tile +1 food per 7 population points.
-+25% normal buildings speed.
-cheap Granaries.
My reasoning: At the cost of Harbors, we get a little enhanced Expansive. +25% normal buildings speed - well, some civilizations were really adaptive to what surrounded them. And I still remember the quote from "Asterix & Obelix", when Obelix said, after waking up in Rome (praetorians caught them sleeping on the wasteland and transported into Rome): "Whew! These Romans are building awful fast..."

Financial:
--50% corporations maintenance cost.
-faster scientific process.
-can rushbuy whenever he pleases (no need for US)
-free tech from the start of each era.
My reasoning: It's something from Scrooge McDuck, and something from Civ3 Scientific, changing Financial into a late gamer. It gives you this - you settle a city, pump cash, and you can make infrastructure quickly!

Industrious:
-+50% to building wonders.
-Engineers give +4 production.
-Double speed to Forge.
My reasoning: I like Industrious as it is. And as some traits have been pumped, this one needed it too.
Imperialistic:
-+50% to Settler production.
-+25% to Military production.
-+100% to Generals.
My reasoning: All the imperialistic empires were military powerhouses. Rome, for example. It seems fit.
Protective:
-+20% to defense (just defense).
-Archery and Gunpowder units get Drill I, City Garrison I.
-cheap walls and castles.
My reasoning: The defense gives you big bonus to a weak trait. You can escort siege units with archers and longbowmen better. You can escort pillagers (they are vulnerable to an attack usually, until Knights and Cavalries). And the rest is the same.
Philosophical:
leave it as it is.
Organized:
--50% civic upkeep cost.
-cheap courthouses.
-workers are working twice as fast.
My reasoning: That's a boost that is... organized. It gives an advantage, but not as awesome as in Civ3. You lay fast roads, you lay more cottages, you cut jungle in just two turns. Now everything is not as long-taking as in Civ3.
Spiritual:
-No Anarchy.
-Cheap religious buildings.
-Monasteries never obsolete.
-100% chance to spread religion.
-+1 happiness from Monument, Temple, state religion, and wonders.
My reasoning: To space an already good trait. (Heck, every trait is good)