But his base/Zoan isnt gonna tag him either and Awakening from Kata would be problematic, heck could he extinguish his flames with mochi?
Not really. His base form has long range attacks - the idea is to keep Katakuri busy and make him exhaust FS, not to hurt him with those.
Flames cannot be extinguished with Mochi, its food bro it's burns and is toast if it touches flames. And King won't simply expose himself to Katakuri like that.
Regarding Katakuri's awakening, we have a sample case in Doffy vs Boundman - except that King is faster than Boundman aerially imo (real actual flight > soru). He can make his way around the Mochi constructs pretty casually, even without the Hybrid form.
And even then, I don't think any of Katakuri's attacks will even pose an issue to King's defense when Zoro's certainly didn't. It's the exact same thing King tried against Zoro in chapter 1032, before engaging him in a sword duel for shits and giggles.