Well, when you put it that way...
Real talk though, I think I'm going to take the L on the 3 main points for now :cheers: partially because I would like to move on to other topics and partially because I'm not feeling motivated to look through WCI and Wano to look for answers as of right now. And mostly because I may not be able to find a proper answer until Carrot makes another move in Wano, and that's something that seems dubious at best right now. If Carrot starts having a conflict with the BMI pirates on Wano then I'll bring this argument back and try to close the loop properly. If I can do that then I feel like I could also give a real connection on why exactly Oda made her pattern unique to other Straw Hats, to justify why Oda would give her a "slight twist". But we'll have to see if Carrot even gets a chance to interact with the BMI pirates.
I can however give my opinion on future developments, though I will preface by saying that it's only a theory right now. I'm not sure of the specifics but what Carrot would have to do to not be a hindrance to the crew is to get a power-up that sheds the disadvantages of Sulong. It's a lot like how Nami's disadvantage with her stick in Alabasta turned into an advantage when she received the Clima Tact.
I actually touched on this before but I can see this power-up happening in Wano due to a potential Rule of 3 situation. And two potential connectors with all of them being Sulong's luck-based downside and Perospero. The pages you see here come from chapters 1006, 1026, and 1027.
1st page is the first point in the rule of 3. Carrot and Wanda are doing fine against Perospero but luck is against them and they lose their Sulong, resulting in their loss. I will label this as Carrot's Ruin. Two other important keys here are that Perospero personally humiliates her about the fight and Pedro in general and that we see Pedro telling Carrot to "keep moving forward." It's also important to note that Wanda has nothing to do with this scene, all the focus is on Carrot.
2nd page is the second point in the rule of 3 when the luck-based downside of Sulong is reinforced, Nekomamushi is about to lose exactly as Carrot did. But on the 3rd page, the moon comes back out just in time allowing Nekomamushi to barely scrape out a win against Perospero. This is an example of what you meant when you mentioned Blackbeard. To control the moon is to control the battle, even someone stronger as Nekomamushi can easily lose a fight if luck is not on his side. It is important to note that Carrot is witnessing this happening in front of her.
5th page is the aftermath of Nekomamushi's battle with Perospero, Carrot gleefully hugs him while Nekomamushi says that she needs to be careful she doesn't turn Sulong. In my opinion that is a reminder to the audience that Carrot is not down and out just yet, she can still fight. I will label this as Carrot's Recovery. Once again, there is only focus on Carrot with no consideration of Wanda's presence.
Now there's only one more point that needs to be discovered which would potentially have something with overcoming Sulong and eventually lead to what I would call Carrot's Redemption. What follows is pure theory with no confirmation so take what I say here with a grain of salt. As for how it will involve Perospero, I would say that it will not be in a 1v1 combat role but more of a Spandam type shit talker/commander role considering his injuries. I'm not quite sure how it will happen if it's even possible, but I see a situation where Perospero regroups with the BMI pirates and causes trouble. Which would lead to Carrot's redeeming moment and finally tie the loop on WCI.
And then I wake up...
I will say though that all of my arguments about Carrot are not ones that would have her join over Yamato, I've been making arguments trying to justify why she could potentially join alongside Yamato.
@jordin put it perfectly in their response to my earlier message. If it's 1 on 1, bet on Yamato. I have some potential talking points about her, but I'm not here trying to prove that Carrot is somehow going to beat out Yamato given the current circumstances. I'm not sure if it changes much, but just know that my focus here is almost completely on Carrot.