I don't think removing the three culture is a good idea. Each policy (aside from Piety) has a way of speeding up future policies, and the Tradition Openers +3 culture is its way of doing it. It ends up being inferior to the Liberty opener if you get a lot of cities early, which is what Liberty encourages. Making you wait for engineering to get aqueducts though is perfectly reasonable. Maybe Oligarchy could lead to Aristocracy and Legalism, Aristocracy to Monarchy and Legalism to Landed Elite. Monarchy is a pretty important happiness boost, so tucking it under Aristocracy would be an indirect nerf.
I disagree on settler growth. Settlers are supposed to be a big investment, a city is its big reward. If you have no more investment in thr Settler than anything else, then that cost/investment isn't quite as high.
What if honor worked like...
Opener: +33% versus barbarians,

culture for kill barbarians, barbarian encampments spawned in revealed territory are shown to you.
Warrior Code: Requires opener. +15%

production of land military units, a free great general appears outside the capital.
Military Tradition: Requires Warrior Code. Units gain 50% more experience from combat and land military units start with Great Generals 1. (A unit built before adopting this policy can get this promotion by upgrading it.)
Professional Army: Requires Military Tradion and Discipline. +15 experience for all newly built military units. Cost of upgrading and purchasing military units is reduced by 33%. Maintenance cost for military units is reduced by 25%.
Disciple: Requires opener. Units receive a +15% combat bonus when adjacent to both an allied unit and the enemy they're fighting. Flanking bonus is 50% greater (meaning 15% instead of 10%).
Military Caste: Requires Disciple. Can construct defensive and experience granting buildings in half the time and experience buildings are maintenance free. +1 local

happiness from these buildings. A garrison increases a cities local

happiness by 2 and culture

by 2.
Finisher: Receive

gold for each enemy unit killed. May purchase Great Generals with faith starting in the industrial era. May purchase units in puppeted cities.
Not sure if that would make it good though. My idea was that by boosting the happiness from garrisons it would make annexing a city less of a happiness hit. The finisher boost letting units get purchased in puppeted cities sounded neat on paper. New units can be summomed close to the front and workers can be bought to improve pillaged lands.