Hm... I like the idea of trying to find a way that the worlds won't all collide horribly, and the struggle involved with trying to actually sort that out. The simulated world that you can't think of as a simulation without disrupting the simulation was a nice touch.
I probably just missed something, but I had trouble wrapping my head around the fact that they had a device that could apparently fix things if they just decided how it worked. If you don't know how it works, then how do you build it? If you don't know how it works, then how do you know that it can work? I guess it didn't seem clear to me through most of the story that it COULD work, and it struck me as two people building sandcastles on a beach to hold back a tsunami, but it will only work if they build just the right sandcastle. Maybe it made total sense to other people, but it seemed to me like they were spending all their waning energy trying to construct a solution without the slightest understanding of the problem--not so much that they just needed more time to try different ideas, but that they were just flailing uselessly in the dark.