The simplest way to balance Marksmen Kog is to give his Ult some OnHit interaction

No, not by making it apply OnHit effects. Being an obnoxious little shit from a screen away is Ezreal's thing.

What I mean is, give the debuff Kog's Ult applies an upgrade. Kick it up to 4 seconds. Make it grant %Missing HP damage OnHit against debuffed targets. Or make it deal one big chunk of %Missing HP damage on his next basic attack. Or make it double-proc OnHit effects on his next basic attack. Something along those lines to make it so his Ult interacts with his basic attacks rather than being pure poke power (or a shitty execute).