The so-called, "collapse of a wave function," is nothing more than a mathematical manipulation, akin to finding the derivative of a function in the calculus. It is not a physical event and it does not cause anything. It is only a way of describing what happens, it does not make anything happen.
But something does happen, Hank: the observation ("collapse of the wave function") causes the probability distribution to change. The wave function gets "reset." And the effect propagates non-locally.
Thus the expectation of classical physics that nature is completely deterministic and perfectly random breaks down. There has been an intervention "from outside," as it were.
You may wish to say that state vector collapse is merely a figment of the imagination, a purely subjective mental construct that has no objective realty. To which I would say: In what way does the classical view of rigid determinism differ qualitatively, epistemologically speaking? It is a "construct," too.
Where did I ever say that QM is "the ultimate explanation of everything?" I'm sure it is not. However, whatever QM is, it is causing a whole lot of rethinking in a whole lot of the scientific disciplines (and other knowledge disciplines as well) about methods and the adequacy of existing theories to give good descriptions of nature.
The search continues....
I just wanted to offer an article which may provide some insight on the subject. I know you have read it, but others may not have: Max Tegmark: Parallel Universes
You and I agree with Max Tegmark on the Level IV which is a form of radical Platonism. But the Level III multi-verse discusses superposition - the wave function collapse, decoherence and Everett's theory (the cat is both dead and alive) --- and why the theory is reaching an anti-climactic point.
betty boop, if you haven't re-read this article since you raised the possibility of an extra time dimension - I strongly suggest you give it another look-see. Your speculation directly addresses what is seen as the flaw of the Level III.