After some soul searching and a few more playthroughs, I've re-updated my personal tier list.
S: Egypt, Poland, Babylon, Carthage, HUNS, AZTEC
The Huns feel like absolute monsters thanks to the increase in barbarian spawning. I already loved them in the past, but now...JEEZ! In fact, all civs who get bonuses from killing are basically buffed, leaving cultural diplomatic civs further in the dust.
A+: Korea, Maya, India, POLYNESIA, SONGHAI, ZULU
Blah blah blah, Moai blah blah. I don't even really need to talk about Polynesia at this point because a certain, swaggy users already talked plenty about them. I love their sea resource bonus though. It really incentives me to take tiny islands when I see them.
A : Mongolia, China, Ethiopia, Spain, Morocco, Indonesia, Assyria, Celts, Rome, Danish, England, BRAZIL
I'll admit I have a personal bias towards Brazil, which is why I admittedly overrated them. I was going to move them from A+ to A- accordingly, but then Gazebo made the Brazilwood camps AWESOME, so they're going to be sitting in A for me.
A-: Russia, Inca, Shoshone, Ottomans, JAPAN, BYZANTIUM, GREECE
I was skeptical about Japan, and I'll admit I'm STILL not fond of being able to outright block tourism, but it's a pretty good new UA for Japan. I think Japan needs something to help compensate for the enemy trade route bonuses they miss out on, like internal route bonuses or bonuses from mutual trade routes, but aside from that, they're okay. They may deserve to be moved a little higher.
I used to rank Byzantium higher, but she honestly doesn't feel too great compared to other civs that get their religion off. The UA is still pretty good, but the rest is just...meh.
I don't get why I've kept Greece in low regards for so long, I just haven't had a playthrough with them in a while I suppose. They're pretty solid in almost most regards however. Diplomacy never really feels troublesome to the point where I wish I had a diplomacy civ, but for what they are, they're probably one of the game's best. And so BEEFY when you get allies.
B+: Netherlands, Japan, France, Portugal, Arabia, Persia, AMERICA, GERMANY, AUSTRIA, SIAM
America gaining golden age points from tile purchases are nice, but considering it doesn't scale per era (IIRC), and golden ages get more expansive subsequently, it doesn't seem as good of a buff as I thought, especially since early golden ages aren't that great in the first place. (Seems like I'm always complaining about America when I show up). The Smitshonian DOESN'T need anymore buffs, so I believe a better buff would be something involving tile purchases. Just throwing it out there, ENEMY TILE BONUSES WOULD BE NEAT! I always think of those tiles as native reservations, similar to the many that are found across America, so maybe they could get a culture and/or gold bonus or fat globs of flat culture. Nothing says "America" like getting culture thanks to what you stole from other civilizations.

Austria, you're still not that great, but I have newfound respect for your UA, because dang it, some of these enemy diplo civs get awfully troublesome. With the kind of influence you can gain early from barb quest, solidifying your hold in a City-State seems easier now if you don't miss your chance.
Gazebo's right, Siam is underrated. They don't necessarily wow me, but the bonus yields they get from allies seems pretty useful, especially if you manage o get an ally early on. The bonus City-State strength is kinda niche depending on the circumstance, but I can definitely see it's use.
B: Sweden, Venice (?), IROQUOIS
It seems like the more I use the Iroquois, the less fond of them I become. I blame bad map placement and a lack of forest in certain areas. There was a good jungle/forest start I had once however, and that was AMAZING. But moments like those are few and far between.
Venice might deserve to be higher. When they get momentum, they're easily A+ material, but if they can't get momentum, they're B- at best. Settling them in B or B+ just feels right.