Kenpachi ain't the highest Zanjutsu title, it's the title given to the strongest of Shinigami. If Kenpachi was for Zanjutsu title then Kurisa would have been Kenpachi over Shiro, hell, Hikari would be the Kenpachi right now. It's a traditional title within Squad eleven, and they're melee fighters. They don't necessarily have to use Zanjutsu to gain it, just so happens that most Kenpachi preferred fighting style is Zanjutsu. You can have a Kenpachi that only uses Hakuda....Yeah. Kenpachi ≠ Highest Zanjutsu title

I'm sure there isn't one for Zanjutsu nor is there one for Hakuda. Simply masters & experts, though I'm sure someone could gain a title/name just like Tenjirō with Hoho, Lightning-Fast Tenjirō. Just like Tabo is known as the man of a thousand techniques due to his immense skill in Zanjutsu. But that's beside the point.
As for contending for the title, well....These are the non-temp Captains (And those that have a chance to become Captains soon due to gaining Bankai): Shiro, Kaizo, Kurisu, Zero, Yu, Hikari, Rio, and Fumio. And since two out of those eight don't/can't use Kido, and the rest seemingly focus more on Zanjutsu/Hakuda. I think the only one to be worried about is Zero when it comes to Captains, or Yu but he also focuses more on Hakuda and Hoho than actual Kido. Zero by far seems the most proficient in Kido out of all of them, but since Gio has access to more Kido and is in a Squad where it's dominantly Kido then he has a better chance of becoming Grand kido chief than the rest. So I wouldn't worry too much, I'd just say focus more on getting Gio to that level rather than worrying about who has to face for that title. His time will come.