For instance, a sequel to "Speed" could be easily disguised, but a sequel to "The Matrix" series would be devilishly hard.
But, I think one of the things mentioned by ChaosTitan -- the reason I wanted to "save" the fanfic was that I'd created a huge number of rich, supporting characters, and I didn't want to lose them. I removed any and all of the "real" characters from the fandom and started fresh. (Started fresh NINE TIMES, but, still, fresh. Okay. Fresh-ish.)
Ok, it's time for me to throw in my 2c - I've never actually been that cagey about the origins of my work.
I wrote a Matrix fanfic back in 2003, banged it out in a couple of days, and killed the OC at the end (but then turned chicken and brought her back to life because I liked her).
Went away and wrote some more crappy LoTR fics.
Wanted to write another story with said OC. Then another, then another. When I looked up two years later, I had three seasons, two co-authors, a small cult and a couple of pieces of fanfic of the series.
At this point I figured I should probably write something original, and began that very painful process of tearing out the original stuff and rewriting the original story.
I cringe at novel versions 1-5 now. I'd managed to introduce some neat new concepts (and a city that I one day hope I'll be able to use again), but it was still too recognisable. Versions 6-9 introduced a few of the elements that I still use now (though those few have been greatly expanded upon).
Around version 10 I think I had lost my mind.
I was totally stuck on these characters (mainly because the OC - now MC - lived in my brain and would poke it with something sharp every time I thought about writing something else).
At this time I had a really, really bad argument about my writing with my boyfriend (now fiancé) about writing and I quit for a long time. I started writing again, but was really nervous, and figured it was a good point to try something new.
A couple of weeks later it was NaNo 2006 and I started writing a story that had been rattling around in my head. It was supposed to be a standalone story that I could get a fresh perspective and go back to what I really wanted to write.
About 10k in, I discovered something...I liked the universe I was writing. I
really liked it. I stopped writing my NaNo and started doing some worldbuilding, and discovered I could write everything that I really wanted to keep into this new world. It was a bolt out of the blue, and it felt really good.
Started two more versions. Another couple of false starts.
Then I finally started writing what I thought would be the final version, everything was falling into place, but it still felt a little weak.
Then I got my laptop.
I don't know what it is about River, maybe she has some inherent magic, but the very first thing I wrote on her turned into my first chapter (a small edit for length and Dorian's peeping-tom-ness), but it was good. Then I banged out more, and I had my start.
It was real, it was good.
I finally don't feel like a fanboy any more, I feel like what I'm writing is my own.
I turned cyberpunk into urban fantasy, gave it a real-world location and set it in the present, but somehow, it still has the essence of the story I wrote five years ago.
(Bizarrely, even though it's urban fantasy, and quite blatant about it, I've had someone liken it to Neuromancer...).