> Is that a request/suggestion or are you just thinking out loud? Because that one looks like an interesting idea I'd totally like to do (if I manage to make up my mind on all the details, names, ages, etc^^)
I guess it's a little bot of both, but if if yo'd like to write it, by all means, please do.
As for the details...
Somewhere half through writing it down an idea occurred to me that maybe it can use Evangelion characters. Asuka would be bragging about her strength, Rei be one to outsmart her, and Shinji sticking around having fun watching the girls have fun and also being the judge. This way Asuka can hang Rei up all the way until she is unconscious and then when she can't hold her anymore Shinji will check if Rei is still alive and remove the noose from her neck. Then in the end I don't think Asuka would accept being outsmarted like that as fun. Not that Asuka minds dying or anything, she's just pissed of by Rei cheating. But Shinji being the judge would declare it's all fair and leave her hanging. Shinji and Rei would probably sit on a nearby bench and watch Asuka hanging while having a casual conversation where Rei tells Shinji how much it hurt in all the details in a tone like it's her most warm and dear memory, and Shinji in the same way tells how beautiful and heartwarming it was to see her in so much pain. Maybe in the course of the conversation they start holding hands and in the end they kiss while Asuka is peeing herself on the background.
If it involves nudity too, then naturally Rei doesn't feel anything about it and Asuka while ashamed strips for the sake of fairness. As for Shinji, while he understands the concept of shame, he also understands how Rei's nudity is innocent and admires it that way, so he chooses to treat it innocently too. Thus Rei probably doesn't get dressed again after being released form the rope and just casually sits there naked with Shinji on the bench and he doesn't say a word about it.
Though I'm not sure if Evangelion characters would fit better then just some random kids as the story calls for younger characters.

And also now half way through writing this another idea came to my mind: maybe instead Asuka was humiliating Shinji for how he is weaker then her even though he is a boy, and they decide to settle it by hanging someone and Rei happens to be nearby and doesn't mind taking part, so they take turns hanging her. Asuka goes first which raises the question of what would they do if she actually succeeds. One option is they'll go for another Rei clone for Shinji to hang, but having clones makes it feel like they're only casual about Rei's death because she's replaceable and not because they're casual about death in general. So another option is just that such a question doesn't occur to anybody until such a case happens and it doesn't happen as Asuka can't hold Rei all the way. Yet another option is that they decide if Asuka succeeds killing Rei, they'll just find someone else for Shinji to hang, say Hikari. But since Asuka fails and Rei ends up alive, they don't need Hikari and just hang Rei again. And this is when Shinji ties his end of the rope and tells Asuka that while she might be stronger, but he is smarter. Now, the relationships here is that Shinji and Rei are more on less in love, whether it's just a fleeting feeling they haven't yet realized themselves, or they've been dating for a while already, and Asuka is just a friend to them. But since nobody cares about pain and death, Shinji enjoys watching Rei agonize and die as it makes him win. Maybe even when Asuka tells that's it's cheating and demands the rope to be untied (not because she cares for Rei of course, just to stop the cheating), Shinji stops her because Rei has to hang all the way to death to prove his method is better. And while Rei is agonizing and dying she is admiring Shinji outsmarting Asuka and is happy for his victory. So when Asuka tries to release her, Rei is also against it.
Though this ends up even further away from the original idea.

Thinking of it again, characters from another one of my favorite animes, Cardcaptor Sakura, could fit as well. As far as I remember when Meiling appeared there was a lot of rivalry between her and Sakura, or rather Meiling was all rivalrous while Sakura was confused about Meiling's attitude. Anyway, let's say Meiling is bragging about her strengths and proposes to hang Sakura to prove it. Sakura doesn't really see a point, but doesn't mind either, so she lets Meiling do it. Then after Meiling fails, Sakura probably isn't the kind of person to hang her back just out of revenge or fairness (like logical Rei does in the first of Eva ideas), so it's probably Meiling who suggests it's now Sakura's turn just to be fair. Alternatively, since Syaoran is probably present and watching (after all it is to him that Meiling wants to prove she is better then Sakura), he might be the one to suggest that it would be fair for Sakura to take her turn hanging Meiling now. Then, coming up with cheating is probably not something Sakura would do either, so let's say Tomoyo, who is also present because she couldn't possibly miss the chance to film Sakura being hanged, mutters in Sakura's ear that she should tie the rope to something. As Sakura does so, Syaoran finds it to be a nice solution and lectures the struggling Meiling on how one shouldn't rely only on brute force. And so Syaroan ends up with Sakura, and Tomoyo is happy for them.
Now, since Tomoyo's in here, maybe instead of naked hanging, she dresses Sakura in one of her fancy costumes that she just carries around all the time in case of filming? And she happens to have more then one with her so she dresses up Meiling too. The costumes themselves though might be something designed to be cute rather then erotic, but in a world where showing off private parts is considered casual (example: http://danbooru.donmai.us/posts/1872844?pool_id=1536 )