As a Shaco main who used to play a ton of eve... sorry to say but you are wrong here.
You are not wrong in that eve is good as ad...
You are just wrong in that she does what shaco does better.
Eve doesn't 100 - 0 carries late game out of no where...
Eve can't hop walls to steal buffs...
Eve can't take a combat summoner on top of smite to be able to fight better.
Eve can't reach out and secure kills on low hp champs with a shiv toss, before kiting back to repeat.
Eve can't give you better map control and vision with boxes.
and lastly, Eve is much easier to catch than Shaco... so her split pushing suffers from that.
Look I like Eve... I think she does a lot right, and I'm glad you are having fun with her, but there are simply some things Shaco does that eve can't hold a candle too.