Well if that's what you consider ruining Zoro's character, I guess it's already ruined.
Chapter 989, Luffy says "I'm going up to take out Kaido!!! You guys handle the rest!!! Watch my back!!!"
Chapter 997, Zoro says "They say Kaido's the toughest guy in the world!! So I'm here to slice him into pieces!!"
Zoro effectively ignores Luffy's orders and decides to focus on Kaido, even though Luffy wants to beat him...
Was Luffy angered about it? No.
The best way to figure out what will happen with Zoro and etcetera is by asking yourself what Zoro's character goals are.
Let's assume we're at a point where Zoro just got healed.
In 1015, everyone learns that Luffy is alive and that he will return to the battle.
But he isn't there yet, Kaido for now is on the loose.
If Zoro is healed *prior* to Luffy's comeback being announced.
Then, given his declarations so far in the arc, he should want to go to Kaido.
He isn't or wouldn't be aware that Yamato is there holding off Kaido.
It would be very uncharacteristic to simply shift his focus to King while allowing Kaido to roam free.
Though, the big assumption here is that Marco stays with King.
If for some reason Marco went away or got defeated, then Zoro's focus shifting to King *could* make sense.
Though, the priorities would still be inconsistent.
In 997, Zoro entrusted others in handling the live floor. Why wouldn't it be the same here again?
If Marco is gone, Kawamatsu and Izo are both people Zoro could entrust in handling King.
If Marco stays with King, then Zoro would rush to Kaido.
Luffy would also naturally want to immediately come back to Kaido.
The timing could play out to be perfect for both Luffy and Zoro to return while Kaido is about to defeat/kill/etcetera Yamato.
Another thing. I think that people just don't understand what "cut down", "slay", or "slice into pieces" means.
In a more literal sense, these are all ways to describing killing.
Though, in One Piece, it wouldn't be incorrect for these terms to be used for defeating someone instead.
I think people see the word cut in "cut down" and see that Zoro cut Kaido, so they think he achieved his goal.
He absolutely did not achieve his goal, he went there to kill/defeat Kaido. He failed, just like Luffy.
He will come back, just like Luffy.
He will achieve his goal, just like Luffy.