And for what it's worth, I'm fond of the artillery platform side of Koggy. It's something that no other champion really boasts aside from Xer, though he does it in a totally different fashion.
Well why not.
I'll toss out a few Innate remake ideas.
For the Tank-Buster some form of True Damage would probably be the best way to go about thing. Corki already gets true damage based on his AD. Vayne gets it from the 3-and-proc system. So does Vel. So how could we give Koggy a True Damage Innate that makes him different from those three champions? Maybe a missing HP based ability?
For the machine gun style, it could be pretty cool of Koggy gained bonus magic damage OnHit equal to some percentage of his missing mana. That would make for some interesting interactions with his Ult. How low do you want to let your mana drop for that extra damage?
And on the Artillery side of things, giving Koggy a MASSIVE attack range boost for a single attack against targets he nailed with one of his skills would be very Thematic. It would make him the undisputed champion of long range Marksmen while still giving his targets ample room for outplaying his widely telegraphed skillshots.