Sadly I do not have the fic, but I DO know a little info. author (at time of fic posting) was going by sesameseed (or a variation, it's been a while) on ao3 and darthtulip on tumblr. I don't remember the title either :(.

And I remember having basically the same reaction, where I didn't really care about the endgame K/T but the scene where he's kind of got a crush on Shane Doan/hooks up with him was way more memorable and despite the whole sad/longing thing I liked it more. In fact, I was thinking about that scene the other day before I saw your comment.