Evelynn idea: new Ultimate "Safe Word" and some changes due to no DFG no more
New R: "Safe Word"
exact same range and aoe of previous ultimate but with new functionality.
Evelynn and all affected targets are suppressed and immune to damage for 3 seconds. (can still chat of course lol)
At the end of the duration, Evelynn's stealth persists through attacking and casting spells, her movement speed is increased by 200% (so it becomes triple normal), and all enemies deal double normal damage to Evelynn, but they can't see her without the aid of a pink ward or oracle elixir.
You could even have a fake tooltip that says "Rumor has it if you say the correct safe word during Evelynn's ultimate, you can escape it faster".
(the safe word is "Please madam, may I have some more?") HEHEHEHE
This would (aside from being ridiculous and awesome) give Evelynn the ability to peel targets away from teamfights for awesome separation. She could use it for temporary invincibility (kinda like zed, fiora, or yi might), and afterwards she gets one of those awesome moments of badassery that leads to epic pentakill moments. Kind of a shame that she doesn't really lend herself to an assassiny lifestyle right now.
With that change, she'd lose a lot of her burst damage including a % health damage skill, but get powerful group crowd control. hard to say what's more powerful, especially when it takes her out of the fight as well. she can whiff completely and end up cc'ing herself leading to a 4v5.
That means that some damage gets pulled away from the ultimate, and with dfg gone, that also means that her q and e can be buffed. Normally an assassin would want to be AD, like zed or akali, or all the others who are ridiculously strong right now. But Evelynn would probably prefer to be AP because she regens mana while stealthed and comes out of nowhere for short, devastating bursts.
So I'd recommend switching E to an AP scaling effect, and letting her go full AP assassin.
Also consider changing her W so that it doesn't break stealth immediately, but doubles the range to detect her if a champion is facing her, as well as temporarily allowing her to be seen by wards. That introduces some counterplay to ward placement and makes it where those wards aren't useless against Evelynn, you just have to consider placing them in different than normal locations.
Also take note that none of these changes break character for her, being a BDSM-centric assassin that thrives on pain and stealth. You may not like her outfit, or her theme, or her voice, but you can agree that if someone went and dramatically changed one of your characters by making them a vampire or a demon you'd be right upset. Evelynn is not one of those. She's a mysterious creature, and might very well be human. Nobody knows because they can't get close enough to her to find out.
The ultimate strengthens her stealth and gives her a rare window of opportunity to use skills while stealthed, and if you catch her ulting in a bush with one of your wards (because she's trying to get away with cc'ing herself for the surprise pentakill), you know to run screaming in another direction. The stealth also gets empowered (and also nerfed) through the W, which severely punishes teams that don't ward (teams that are probably already losing a lot of games but don't understand why because ward benefits are invisible until you see how well they help you). If you don't have any stealth wards up against this version of Eve, you will get wrecked when she dashes for you from behind, remaining stealthed.
I know there are a lot of players out there who hate that Evelynn is permastealthed, and neuters the effectiveness of wards (because it's hard to justify 75g on something that does nothing, and you only get one pink ward). I'm hoping that changes like this would win you over because they offer you an opportunity to get more than the normal value out of those stealth wards.
I'm also hoping that this ultimate is a lot more exciting and thematic and fun, because it offers a lot of counterplay. If you see Eve, and she's hiding in a bush, you can bait her into ulting at the wrong time, and timing stuff like your aoe and beam skills to hit right as she comes out of that ult. Then it's a very intense game of timing, skill, and movement to get kills. I don't know about you but that sounds a lot more fun than an ult that gives her a shield and a bit more damage.
TL;DR: W causes Eve to not break stealth, but she can be seen by wards (!) and champs can see her easier if they're looking in her direction. E uses AP. R causes Eve and others to be CC'ed and immune to damage for 3 secs, then she stays stealthed while attacking and everyone takes tons of damage (even her).