The "Bad Dream" story by Rosie reminded me of that little idea I had. I probably won't write it myself, so feel free to pick it up or adapt it to other characters. As I based it on Evangelion, but apart from the ending with clones it can probably be used with any characters really.

Killing Snore

So, the core of the idea is Shinji staying for the night at Rei's place. Maybe their relationships have progressed enough and they have some passionate sex before the actual sleep. Or maybe it's a totally innocent friendly sleepover. In any case Shinji discovers that Rei actually... snores like a train. And he can't get any sleep with that sound. So he casually decides she won't snore if she doesn't breath and smothers her with a pillow. Or, another option, puts a plastic bag on her head, but that would probably be hard to do without waking her up. Unless you want him to wake her up, tell her how her snoring doesn't let him sleep and they come with that solution together, again quite casually. Anyway, Rei suffocates and doesn't snore anymore, so Shinji sleeps peacefully for the rest of the night next to her cooling body. Happy end. Or not, if you can come up with any ideas how to continue it, like show his reaction when he wakes up in the morning. Like, maybe he finally realizes what he's done and is terrified by it (which would fit better with the option where he smothered her with a pillow without waking her up). Or, for the option where he did wake her up and they were both casual about making her suffocate for his peaceful sleep (though this ending would work for the first option as well, maybe even better, being not entirely expected), he wakes up still being casual about it and a new Rei clone comes in, having all the memories of the dead one and also being totally casual about it, and they casually dispose of the body and go to school, both agreeing that this method of fighting the snoring worked very well and next time Shinji is sleeping at her place (which would probably become regular in the scenario where they have a relationship) he should just smother her right away before going to sleep instead of struggling with sleep for half of the night.