I like this theory, I like it a lot actually.

I've always assumed the blank in the blight is actually a city. We've even seen a hint at a city in Towers of Midnight, when Perrin comes across the spot of blight with a strange looking tent or something that had switched places with normal land.

I think that's also how Trollocs were randomly popping up too. Just like the hallway switches we've seen, I think spots of land are switching.

However, back to your theory. It would work, and would make since that Alivia will kill Rand if she thinks he's actually Morridin. I hate the body swap theory, but it does work on a lot of levels. Rand as Moridin could kill his old body, making everyone weep which fulfulls black prophecy, then Alivia could kill Rand, which will allow them to switch back in T'A'R.