Oda never really broke conventions with SH recruitment. None of the SHs had the exact same recruitment but all of them, including Jinbe, shared the formula of having:
-a backstory
-a main villain tied to them
-having Luffy defeat the big bad for them
-being one of the most important parts of the arc
-strong thematic ties to the arc
Carrot has none of those so I don't see the reason why Oda would break something so major for the first time ever, especially just for Carrot.
These 2 sections can be addressed at once.
Pedro wanted to go with Roger and see the dawn, but was rejected for being too young. Roger told him "everyone has their time to shine" so Pedro was waiting for his. Pedro flat out begged for his life saying that he must live to see the dawn, and did everything he could such as hunt Poneglyphs, to support the ones who would bring the dawn.
Pedro left with Luffy simply cause he wanted to repay Sanji, the being with the SHs convinced him that they will be the ones to bring the dawn, and told Carrot that someday she will learn the importance of the SHs finishing their voyage. With that, he finally got his time to shine by sacrificing himself and becoming the pillar for the SHs brining the down.
Inheriting will doesn't have to involve becoming a SH though. We've seen plenty of characters, including ones who traveled with the SHs, inherit the wills of those from the past and never joined.
Pedro's wish was for the dawn to come, and his will is being a support for those who will bring the dawn.
Nothing really suggests WCI was a set up for Carrot given how she played no big role in the arc. She was a supporting character at best. Her best contribution to the arc was delaying the BMP, just like Jinbe, Sanji, Nami, Chopper, Brooke and the Fishman Pirates did, not to mention that she was used as a hype tool and expedition drop for Sulong.
Your idea of a satisfying conclusion for Carrot is entirely subjective, as is mine. Many characters were given conclusions deemed unsatisfactory by the fanbase, and Carrot doesn't need to be a SH to have a proper conclusion.
So yeah. Pedro never really thought he had to join the ones who will bring the dawn. He just needed his moment to shine in supporting them.
Pedro told Carrot to keep moving forward and that everyone has their time to shine, something Carrot repeatedly fumbled over. His words played in her head with Katakuri, Daifuku and Pero, and all 3 times she failed. It wasn't hee time to shine but the Dukes presented her with her moment, poor writing n' all. As seen with Pedro's will, you only need to support those who will bring the dawn. Just by seeing the dawn after the SHs bring it is she completing Pedro's will.
Yes Carrot wasn't developed at all at being a leader and it still a shitty resolution if it is, but that wouldn't be the first time Oda has done that. Many plot points in Wano didn't even get a resolution.
If I missed some things then apologies cause typing this out was pretty tedious for me.