If observing a dead cat causes the waveform to collapse such that the cat is dead,

Unless I've misunderstood the Copenhagen interpretation, it doesn't. (Then again, it's not a brilliantly well-defined interpretation to start with.) It's not that one observes X and therefore compels the wavefunction to collapse to state X rather than state Y; it's that observation provokes collapse to a random eigenstate, and the result of the collapse determines the result of the observation (not the other way round). As such, you can't derive the statement that P(D) = P(D) + P(M)(1-P(D)), and so there's no constraint forcing P(D) = 1.