What can be done with Karthus?

With this mage update coming up I'm in favor of having more of this particular champion having something a little extra. Granted he's categorized as the "press R to win/pentakill" guy, I think he's missing a lot to his kit. What can be added to him that will make him better? I will try to add something to each of his abilities and hopefully something strikes. I will not be biased because he's my main but at the same time I'm wanting Riot to throw him a "bone" (Aha, pre-rework jokes. Why do I have friends?) so my suggestions are.

Q - Basically his most reliable damage source for the whole game because it's maxed first. Honestly the spell is fine the way it is. But, with what I said earlier, if there's any way to improve something why not go off on that? So what could be done with his Q? I was thinking something along the lines of amplifying damage with consistently landing them on champions up to a stack mechanic. It sounds a bit overboard but with a max damage cap to balance it to the point it's not super ridiculous it would be tolerable, perhaps even cost more mana with every stack. Also gives enemies more the reason to dodge against him and place them strategically as him.

W - This ability was recently nerfed from what I understand. For the spot this one is in, it's his last maxed spell with some utility. Maybe the most that can be done with this is refresh it upon death. Sometimes it feels awkward having it on CD as you're about to die/already dead.

E - This one I came prepared for. If the mana restoration could be redeemed while it's active that would feel nice. It would help with his poor damage early game, and it would just feel right. It might feel too much like Swain but at the same time it doesn't feel too good to go oom trying to wave clear in general. I see this one being the most realistic change.

R - Everyone's favorite. My thoughts on this are that not everyone will like the idea of this even being buffed. But let's be honest... 3:20 seconds is probably the highest cooldown on any ultimate in the game (correct me if I'm wrong), and there's probably a good reason why. But Soraka has a reverse version of Karthus' ultimate having like 1/3 of the cooldown timer that is as justified as my reason for this much-needed change. To be fair it's supposed to reward for a good timing on the ultimate rather than just buffing it for free in general. My idea for this one is... Getting a cooldown deduction by 5% for each kill and assist (up to 25%), I have no clue whatsoever what kind of items or item reworks are coming with the mage update but I have a hunch that his core item path will still lack CDR stats of any sort. With this change, it gives every R a much truer purpose than just seeing how much damage you can do. The only reward with it's use is securing a kill, and it seems hollow. People need to understand that in a perfect game this would be broken but more times than not you have uncoordinated teams that sometimes forget the potential in a teammate Karthus. If you're lucky you'll get the full 25% deduction. That's 80 seconds level 6, 45 seconds at level 11, and 40 at level 16. Most times it will be 5%, or 10%, and it will reward your resources in some shape or form regardless. That's what his ult really needs without making it extremely overboard.

If any of these can be implemented then I will die happy (I mean technically still live 7 seconds to spam ctrl 3 in zombie passive form, but you get me). I understand not all of it will but if I can be a contribution to better to one champion... Any of the above I feel would give Karthus an up-to-date and meaningful fix to today's game standards. I would like to be enlightened on other ideas to buff this particular champion if someone has any. Keep it civil.