I stand by my early sentiment that Neeko should have been a battlemage, not a burst mage. Give her self-healing and sustain, not insane burst. It would fit with her nature theme and enhance her ability to actually take trades using her passive. If you transform into somebody to bait in an enemy, surprise! It's Neeko... aaand you killed her anyway because she is paper. A battlemage playstyle would suit her so much better.
Weigh her Q damage onto the last explosion, not the first, but amp up that damage considerably. This would reward landing both skillshots and proper wave management to get the most out of her damage. Have it heal Neeko with each pulse when she stands inside the zone, counting as a hero hit, giving her a new way to waveclear and sustain as well as a form of protection when she gets dove.
Have her W passive heal Neeko on that third hit instead of dealing damage, increased against champions.
Have her E also reduce enemy damage output for a short duration.
Tone down the damage of her R, but have it leave a zone of spiritual magic that heals Neeko and her allies while they stand inside it, while slowing enemies in the zone.
Done. Battlemage. She'd have less damage, but would be considerably safer and harder to kill, able to sustain through teamfights and offer sustained AoE damage, like a battlemage should.