Time to give Kog a real identity
Machine Gun Kog got reverted. Artillery Kog got gutted and it doesn't look like he's coming back (RIP AP Koggles). So that leaves one identity left in Kog's kit that hasn't been explored. A team-focused Tank Buster, as opposed to a selfish Tank Buster like Vayne. A champ with good personal damage who more importantly focuses on amping the damage of his team so that utility focused comps that would otherwise be unviable suddenly have the damage they need to succeed. Not only would this give Kog a unique niche among Marksmen, but it would fit perfectly with Riot's declared vision for Kog that he's the Marksmen you're supposed to build a high utility team around. It would also fit perfectly with his corrosive theme. So that said I give you Kog'Maw, the Acid Damage Carry.
Objective: Provide Kog'Maw with a unique niche among Marksmen and further cement his role as a team-focused champion rather than a selfish one. While Kog'Maw's damage is strong, his greatest strength should lay in amplifying allied damage against enemy champions.
Passive - Eldritch Acid: Kog'Maw's basic attacks and spells apply stacks of Eldritch Acid to enemy units for four seconds. Each stack of Eldritch Acid reduces flat resistance by (amount), stacking up to (number) times.
Q - Caustic Spittle: (Passive IAS removed. Cooldown lowered dramatically and damage adjusted.) Kog'Maw fires a projectile that deals damage and applies the Corroded debuff for four seconds. While Corroded, Eldritch Acid stacks shred (percentage) resist with the passive flat value as the minimum amount. Consecutive applications of Eldritch Acid increases the strength of the percentile shred.
W - Bio Arcane Barrage: (As live. OnHit damage might need to be adjusted.)
E - Void Ooze: (Slow increased to 50%? 555%? at all levels, level 1 cooldown dramatically increased and scales down with level. Kog needs a functional one-point-wonder utility skill like other ADCs have access to.)
R - Living Artillery: (Base damage adjusted, effects against low HP targets removed.) Kog'Maw fires an artillery shell at extreme range, dealing magic damage to enemy units hit and applying the Free Food debuff for 4 seconds. Debuffed targets are revealed for four seconds and take (amount) additional magic damage on every instance of allied damage against them. This effect can proc up to (number) times per application.
Welp. There it is. Kog's artillery poke and machine gunning are still gone, but instead he gets access to powerful tools for amplifying allied damage. His new passive, Q, and R actually encourage keeping him alive for as long as possible since his damage is largely back-ended. The longer Kog stays alive, the more he can wreck enemy defense while providing his team with vision and amped damage. The kit as a whole fits together thematically and in terms of the gameplay it encourages. Kog's range still supports the fun Trinity kite-and-poke style that Kog has always been known for, but now he has something to actually set him far apart from the other Spellblade ADCs. More importantly, Kog still wouldn't be a fit for all teams. High damage comps against mostly smooshy targets wouldn't need his damage amplification at all. A Marksmen with greater CC-based utility would probably be more desirable in that case. Kog would still be a niche champion and his niche would be much more strongly defined.
Given everything else Kog has gone through at this point, I feel this remake (or at least something like it) would be the most interesting, most healthy direction to take Kog in.