I dunno about you, but old Sion was a disastrous mess that had no cohesion within his kit and had no connectivity with his lore.
Old Sion was a fusion of aspects from Abaddon and Leoric with a built-in Armlet of Mordiggian to top it off. He was a combination of a number Dota heroes that Guinsoo made and the kit-goal was to make an undead fighter who was a threat via his massive lifesteal helping to keep his allies alive. The shield and stun where originally intended to simply help him do that job.
Mage Sion became a thing when it became obvious that melee champions without gap-closers had a ton of trouble getting within range of Trist, Ashe, and Ezreal to whollop on them. He didn't need to get into melee range to drop respectable burst on a moderate cooldown. Something as simple as swapping out the AP ratios on his skills for AD ratios ala Yi's remake would have preserved both playstyles that Sion players actually enjoyed.
This game is about gameplay. And sacrificing gameplay for abstract ideals like 'cohesiveness' and 'lore connectivity' strikes me as somewhat silly.
As for what to keep, I think her passive is her most unique aspect, and should probably be the building block for a new kit.
Goodness, how many times does this have to be said?
So long as Eve has her current passive the rest of her kit will suffer markedly for it. So long as she can freely bypass wards the rest of her kit is going to be a watered down mess.
You want some kit cohesiveness? Here you go.
Eve is a Baobhan sith from the shadow isles, a seductive, razor-clawed undead monster that entices and beguiles unwary travelers before leading them to secluded areas and devouring them. Push her visual appearance toward elegant and predatory and away from BDSM.
Innate- Malice and Spite: Eve feeds on the life-energy of those she slays, healing herself for (large amount that scales by her level) HP on kills and assists.
Q- Hate Spike: Eve spikes two nearby foes with malevolent magic, dealing damage and sapping their vitality. (Prioritizes Eve's auto-attack target, has built in spellvamp).
W- Beguiling Kiss: Eve kisses a nearby foe, clouding their mind with glamour. The target is Charmed for two seconds, is removed from allied vision, and becomes invisible to allied minions and wards for 4/6/8/10/12 seconds. During this time the Beguiled target can't send pings.
E- Ravage: Eve lashes out with her claws, dealing damage and reducing the target's armor and magic resist.
R- Shadow Walk: Upon activation Eve stealths for up to 6/8/10 seconds and gains a movespeed and attack speed buff for 10 seconds. This ability refreshes on kills and assists as Eve feeds upon the vigor of fallen foes.
There you go. Has a kit founded in her lore, unique and interesting mechanics, and cements her role as league's deceptively tanky life-stealing vampire thing.