(there's a small nsfw right at the end by the way)
Coming back to Zosan, I think Zoro (and the strawhats honestly) would be like. Really set on trying to make Sanji purr.
I really like the idea that omegas only purr when they are really happy, relaxed and feeling safe, so even before Zoro starts courting Sanji (properly, cause instigating fights is Not a valid courting technique no matter what Zoro says [it works, cause they're freaks]), he's dead set on making him purr because making sure the crew feels safe is his job, so if Sanji doesn't purr = not feeling safe, and if Sanji not feeling safe = Zoro's not doing his job properly. So he does a lot of stuff from like, guarding the galley when he's making food to actively growling at anyone who dares look at Sanji wrong. They still fight and argue all the damn time, but Zoro makes it his mission to build Sanji the most safe most secure nest of all when he notices the cook is in pre heat (in my head, nests are made in really small and dark spots, like a closet), so he spends a whole day cleaning the closet in the boys' room and filling it with the crews clothes, and be does all that even before Sanji himself notices he's in pre heat. Sanji knows right away it's not a courting gift cause it has all of the crews clothes, but he looks at the nest and he almost starts crying. It's the first nest someone has built him (aside from Zeff, but that's his dad so it doesn't really count), and the attention the shitty swordsman put on it is like. So much. He makes sure to put bedsheets on the floor so the clothes and pillows aren't in direct contact with it, and then he makes sure to cushion on of the sides more, so Sanji has a place to rest his head, he stashed a few water bottles there, as well as extra bedsheets and some spare pajamas and loose clothes (if Sanji steals more shirts from the swordsman to use during his actual heat it's no ones business). But. The cook still doesn't purr, so Zoro keeps doing shit. And then Whole cake happens and it's actually the worst, cause Sanji is really stressed all the time and he's growling and Zoro doesn't know what to do so he just. Builds a little nest inside closet of the room that's supposed to be for the first mate (Zoro think he's never used it) and just grabs Sanji like a sack of potatoes one day and brings him there. He makes the cook stay in the nest and he's So Gentle. He takes Sanji's shoes and tie off, opens a few buttons to let his shirt a bit looser (they're fighting the whole time by the way, but not really fighting cause Sanji sort of sags from exhaustion and lets Zoro do whatever), so he bundles the cook like an omega burrito, and stays there with him guarding him from the outside.
And that's the first time Zoro has ever heard Sanji purr, and it starts as a slow thing, but it kinda explodes from there (if you've ever heard an old car, it starts really low, and then it gets Really loud). And then Zoro starts hearing he purr Everywhere, not just when they're alone, but whenever the two of them are together by themselves (which starts happening a lot more after that first time) he's especially loud.
And when Sanji lets Zoro hold him to his chest? It's the best feeling ever, cause Zoro can feel it with his whole body just how happy and content Sanji is.
(it's especially good after they start fucking, cause Sanji gets really malleable after the first round, but after Zoro's really done with him, Sanji's purr gets really loud and he's just sooo relaxed, sometimes Zoro gets one more round out him when's like that, and he purrs the whole time)
Omgg I also love omegas only purring when they're happy and/or relaxed. (I also like to think alphas have a very similar instinct to purr and in a lot of cases do it to spur their pack to purr. You know how when a wolf howls it starts a pack wide howl ? Like that lol)
The second it dawns on Zoro that he's never heard Sanji purr it immediately becomes a problem. Zoro isn't even fully aware of his feelings for the cook, but he takes Sanji not purring for his pack as a serious challenge and is fully dedicated to changing that.
Maybe it's because Zoro lacked a proper pack growing up, but any time one of his crew members doesn't participate in pack behavior it's like physically painful for him (which is one of the reasons why it took so long for him to realize how he felt for Sanji). Like whenever someone is not happy his little alpha brain is like 'you failed them.' and it stresses him out. Sanji always makes sure to scent the crew and he makes their pack nest, so at first the purring problem isn't really noticed. It's probably not until the first time he hears his other pack mates purr together that he realizes Sanji isn't joining in.
Once he actually understands how he feels about Sanji that need gets so much worse, like he's starting to look a bit pathetic with how desperate he's getting. Especially when he starts making the nests, he's never cared for cleanliness of being neat but all the sudden he needs everything to be perfect for Sanji.
I bet Zoro was silently fist pumping as soon as Sanji started purring the first time, like that such an accomplishment. Not only did he get a pack member to purr, he's also the first (and for a while only) person who's gotten to hear Sanji purr on the ship.
(Sanji is Zoro's personal vibrator and he's got a Big motor on him, like you can feel it all throughout his body lol. After being mates for a while Zoro kind of worries they might make some pavlovian response to his purr because hearing it out of the bedroom makes him twitchy.)