The problems balancing Eve come from her charm and the need for reaction to assassin burst combos. Because the charm arrow indicator only shows up once the charm is already fully primed, the reaction time against her has to be gated by her stealth radius and movement speed.
Since she didn't have a typical assassin rotation in her prior form- R into E for good upfront damage, but then Q followups that added persistent damage- She didn't need such reaction time necessary. She couldn't outright burst someone down with a full combo and had to always clean up and chase with Q, giving plenty of time to react after the initial burst.
With her new kit, she's a balancing nightmare, going to be either worthless or broken as hell based on the damage numbers she has in any given patch.
Before any other change can be made, she needs her charm indicator arrow moved forward in the charm timer. If the arrow showed up after 1 second instead of after 2.5, Evelynn's opponents would always have a consistent 1.5 seconds to react to her location when she goes for her combo, no matter how fast she moves or how small her stealth radius is. Conversely, by weakening her full combo in this way, it shores up powerbudget for the rest of her kit, opening up areas for change that could make her feel better or more in line with her older self.
So, changes I'd want as a former Eve player--
Base stats
Movement Speed 335 -> 345
Along with her passive change below, this is designed to give her some better early camp routing
Passive:
Stealth detection radius decreases with level, becoming smaller than even her prerework radius at level 17 and 18
In the later game, Evelynn has an awful time picking targets out of an organized group. By lowering her stealth break range as the game goes on, she has more opportunity to at the least go one-for-one with a key target.
NEW!: While Stealthed, Evelynn's base movement speed is reduced by 10.
Compensation for the change to her base speed
W
NEW!: Evelynn gains 25/35/45/55/65% movement speed toward her W-marked target
Cast Range: 1200/1300/1400/1500/1600 -> 1100/1150/1200/1250/1300
Charm arrow appearance after: 2.5s -> 1s
E
Magic Damage: 30/40/50/60/70 +4% (+3% per 100 AP) of the target's max health -> 20 (+50/60/70/80/90% AD) + 4% (+3% per 100 AP) of the target's max health
Empowered E
NEW: hits the target three times rapidly, applying on-hit effects and traveling with the target
Magic Damage per hit: 15 (+15/25/35/45/55% AD) + 3% (+2% per 100 AP) of the target's max health
Giving Evelynn her on-hit procs and synergy with gunblade back. Numbers listed might be too strong