All excellent ideas guys, and thanks for the input.
Anti-existence as it's being used here is supposed to be something like the opposite side of a coin. Logic would dictate that you can't have a part of one side of the coin existing on the other side, but when it comes to dimensional anomalies (something you see quite often in Nanoha) the laws of physics, magic, and the universe tend to get thrown completely out of whack. Think of it as if your shadow suddenly jumped up off the ground and started walking around on its' own.
If I were aiming to turn this into something like Evangelion, P.H., I'd take your advice on this and figure out some way to incorporate Anti-existence as a doomsday-style plot device. Here, however, as Munchkin put it, "It's my universe. I'll do whatever the hell I want to with it."