So when I woke up this morning, I realized something: this is a great idea.
I wouldn't actually do it with Pulp Fiction, because I don't think there's any way that you could destroy the whole movie with a single additional scene, but it would definitely work with some other movies. The trick, I think, would be to get movies that people actually know the ending to, and that are at least somewhat beloved. Here are some examples for your consideration. Some spoilers follow, but if you don't know these by now, you probably don't care that much.
In the alternate ending to Return of the Jedi, Darth Vader lives, everyone forgives him, and he and Luke have lots of happy times together.
In the alternate ending to American History X, the protagonist's brother doesn't get shot, and they final scene features the two of them tearing down the white power propaganda in his room together.
George Bailey realizes that even though he's made life better for a lot of other people, that doesn't change the fact that his own life is still completely miserable, and exactly a year after coming back, he takes his life on Christmas Eve, this time for good.
Ebeneezer Scrooge doesn't change his ways at all; seeing his own imminent death and all the things he's lost makes him even more spiteful and petty. This one would actually be pretty easy to pull off, because new versions of A Christmas Carol are made every year (for some reason).
Planet of the Apes ends with Heston running to the beach, where he sees a spaceship light up its landing thrusters; the rescue mission has finally arrived to bring him back to Earth.
Beatrix gets back together with Bill, and they set aside their differences to raise their daughter together.
The new ending to Watchmen features Rorschach and Night Owl stopping Ozymandias in the nick of time.