So sometime after the experiment starts we magically stop the clock on the wall of the universe. Since we are at a particular point the cat is either alive or dead, let's say dead.

If we stop time, we do not find ourselves at a "a particular point [where] the cat is either alive or dead". If we stop time, we find ourselves at a point in the configuration space. At this point in configuration space, the different possible configurations have different amplitudes. Some of these configurations include the cat being alive, and some include the cat being dead.