Some Ideas for Karthus

As of right now, it looks very clear that Karthus isn't going to go the way of Twitch anytime soon. The fact of the matter is that Karthus is in a very poor state right now. But all in all, his kit for the most part is solid, there is just two problems, he has no escape, and his ultimate is very very unreliable. Some ideas that I thought of for some tweaks in his kit to increase his survivability were to make his wall of pain either increase his movement speed when he walks through it, or turns him into his zombie form for a short time, granting him invulnerability. The second idea I thought of was having his ultimate be an execute. This I know is something that could end up being very very unbalanced, but if tuned properly, it can work very well, because as it stands right now, his ultimate is not up to snuff in terms of damage output vs cooldown. My idea for it would be to give it 100% AP scaling, and have it execute champions at X health, + 1 health per AP, so that late game Karthus can be a lot more substantial. These are just ideas.