@Slamu
I like this, but I think sourcing the lumber is supposed to be day 1, leaving two slots there.
I like the justification for Zoro being there. Vivi would be there for another perspective.
@Ompa60
I feel like your write-in puts a bit much on Taylor.
She's asking for Nami and Zoro's help, which is good. Nami is savvy and Zoro is straight forward. Both good perspectives to have.
They might need reasons to want to help. Maybe not, Taylor wanting to help may well be enough on its own, but having reasons that might appeal to them in mind if needed wouldn't hurt.
But there isn't going to be time for befriending, stories, etc. all as a set up to the actual conversation...all within the span of a day or two.
Plus it's Taylor. Her social skills are trash right now. She'd come off as awkward at best. Sudden changes in friendliness from her or Nami will likely make her be on guard, especially when it's time to talk to her directly. The Straw Hats are easy mode for Taylor, but Vivi is under cover and on guard.
It actually does feel like canon Taylor in that part. Trying to control the conversation by subtle manipulation and setting the stage ahead of time. But that isn't a good thing.
We ask for Nami and Zoro's input. That means ceding some control to them.
I'd also suggest cutting out the part about how to get Vivi away from Mr. 9 for a chat. Keep it non-specific which will let the three of them figure it out. This also allows Zoro to possibly be there too.
--[] Broach the topic with Nami and Zoro, tell them everything you know about Alabasta's situation and get their help with planning the talk with Vivi.
---[] If they need motivation besides sympathizing with Vivi or Alabasta and wanting to help, or that you want to (which is fair, it's a big ask and Vivi is a stranger)...well, Baroque Works offers a lot of challenges and their members also happen to clearly be bullies who deserve a thrashing. And as royalty, Vivi is rich, she'd surely be grateful to those that help her and her kingdom, right? Maybe monetarily grateful. And you can take Baroque Works' stuff.
--[] The talk should be done away from Mr. 9 since Vivi obviously hasn't revealed her identity to him yet.
--[] Reveal you know her identity with the excuse of keeping track of the noble lineages that attend the Levely every 4 years (if you need an excuse at all)
--[] Lean into your shared idealism. Both yourself and Vivi want to make the world a better place, even if for Vivi it's just her own kingdom for now.
--[] They can also draw on the Straw Hats' exploits. To highlight their abilities, and also their inclination toawards fighting pirates that hurt or oppress civilians. Arlong Park and Clockwork Island should especially resonate with Vivi's plight. You won't ask Nami to get personal on the former unless she wants to.
--[] The goal is to get her to accept our help and get as much info about Baroque works as possible. If successful, she should ask Luffy for help directly (not that his response is really in doubt, it's an adventure that involves punching jerks in the face with a victory feast among the likely rewards, but he's still the captain and should be the one that decides to set course for Alabasta)