I can't do Death Note, because that's too tightly plotted for me to feel comfortable with slipping something in and I don't think I have a good sense of either character. RPS is pretty much one fandom in my mind and I've written lots of that. I've technically written Star Wars before, but that might be a good choice. I don't have a good handle on the LotR world. Minority Report is too contained and I don't really like any of the characters enough. Hmm. I'll think about it.
Oh, and a Star Wars rec:
For What you Dream Of - vaguely implied Obi-Wan/Anakin (it's one of those blink-and-you'll-miss-it type of things), but yeah. A mission to Obi-Wan's Jed-hostile home planet and revelations of his past. It has a gorgeous mood and an understated feel. I wish I could write like this. Seriously.