Nerf Kog's W and Buff his Q?
Yep. Sounds good to me.
Bio-Arcane Barrage loses the %HP damage. Keeps the flat OnHit damage, however. The flat damage would probably need to be adjusted once the dust settles to find a good balance point.
And Q becomes...
Caustic Spittle Active: Kog'Maw's next basic attack deals (percentage) of the target's maximum HP in bonus magic damage OnHit. Additionally, it shreds (percentage) of the target's resistance.
But why? At the moment, Kog has WAY too much damage packed into his W. Before he got his passive Q attack speed moved over, he was okay at best. Splitting his power delayed his power spike until later in the game. And a weaker early game means it was harder for Kog to really get rolling. By moving a good chunk of that power to his Q (and gating his %HP damage behind cooldown) we lower Kog's damage potential while also making his Q a much more attractive ability to level up. It also makes Q Kog's designated tank-busting skill, so there are clear benefits and downsides to leveling up one or the other first. Further, I went with an attack modifier because the present form of Q really doesn't mesh well with the rest of Kog's kit. It's just sort of... there. It made much more sense on artillery Kog, not so much on machine-gun turret Kog. This would allow Kog to use his Q whilst doing what he's already doing, spewing damage everywhere.
So that's one idea.
Any other thoughts on what to do, aside from rolling Kog back to 5.22 (or 5.20...)?