This newest design looks more representative of Teddy's entire presidency, rather than just the conservationist aspect, which I think is a good idea. However, I still find a few faults with it that I'd like to offer some constructive criticism for.
UA: I understand that the first half of the UA is probably based upon the Spanish-American war, but I don't quite like that bonus for attacking warmongers. The USS Maine probably wasn't attacked by Spain and most likely sunk due to an accident. Of course the media at the time claimed Spain did it and so did the imperialists, but I still think it's kind of an odd bonus. It's also kind of weird since Teddy and American imperialists in general at the time weren't going around crusading and liberating subjugated peoples from an oppressive power. I think something that might be more appropriate of the American imperialist period would be a bonus from liberating cities. After the Spanish-American war, Cuba won independence (although it was basically an American protectorate), and Puerto Rico, Guam, and the Philippines were taken away from Spain and turned into US territories. Also, the most notable of Teddy's accomplishments, the Panama Canal, was possible because he supported Panamanian independence from Colombia in order to be able to get the local government to approve and build the canal. It something that makes sense to me and there's probably some kind of interesting stuff that could be done with imperialistically liberating cities.
Also, out of pure curiosity how did you decide upon the number 22%, same with the 11% for the Rough Riders? Why so specific? Almost all vanilla and mod modifiers are multiples of 5 so I just find that odd.
I like the idea of getting a bonus for protecting city states, however I feel that it's too underpowered. The +1 Happiness isn't really too impactful and the defense boost they get is only useful in the early game. Plus, I just find protecting city states to be kind of boring, you don't need to do anything besides discover them and press a button. How about something more powerful like perhaps bullying city states for gold doesn't reduce influence? It allows you to keep that same kind of stranglehold on city states, but in a way that encourages actually sending forces to city states and provides a bigger benefit.
UU: I like the first half, but the second I find really bad. How often is that scenario gonna happen? I understand how it's supposed to be placed within city state borders like a peacekeeping force and then used to defend them, but I don't necessarily think they need to be on Alert to do so. How about just giving them a straight up combat boost in city state borders or near city state you've pledged to protect? That keeps the same concept while being more accessible.
Also, I think the White Fleet could work here too, especially if you added something regarding bullying or intimidating city states. They would allow you to maintain a force near city states more easily and quickly, and would be a powerful combination with Gunboat Diplomacy from Autocracy. I wouldn't say the White Fleet needs less movement as suggested by your prior design though. I would also argue that they could be an earlier Battleship replacement rather than a Destroyer since the Great White Fleet was composed of predreadnoughts, and the dreadnought is a battleship replacement for JFD's Churchill. I also think the White Fleet would be a cool thing to have historically since Teddy was influenced a lot by Mahan's "Influence of Sea Power upon History" so Teddy getting a naval unit is extremely fitting in my opinion.
UB: Nothing fancy but it serves its purpose. I would suggest adding that it may be built in cities with natural wonders instead of just freshwater cities to make it more versatile. I feel like it could be fleshed out a bit more though. I also just thought of how city states tend to have natural wonders in their borders. I'm just imagining how funny it would be to see people playing as Teddy invading city states for their natural wonders.
Anyway, I hope you don't take the feedback harshly or feel that I suggested an overhaul, I just really like Teddy Roosevelt

. Also, if you get around to making this and need any help, feel free to let me know, I've been wanting a Teddy civ for a long time now and love to help.