That's not how the double-slit experiment works. Both slits remain open at all times. The detector only detects the passage of the particle through one of the slits.
Right.
I'm not saying I'm an expert, or even that I'm remotely intriguied by Interacting Many Worlds.
My point is, as long as the photon(s) have been undetected, they can travel through both slits.
As soon as you detect the photon at one of the slits, it cannot, as it has been measured at one of the slits.
This is the first explanation of a 'many worlds' theory of quantum mechanics that has ever made sense to me. The animations are excellent:
http://www.preposterousuniverse.com/blog/2014/12/16/guest-post-chip-sebens-on-the-many-interacting-worlds-approach-to-quantum-mechanics/