Hysteresis exists. Complex models are often time-dependent, and initial states may not always be retrievable under any circumstances.

In the immediate sense, the world we experience obviously has the quality of irreversible change. On a larger scale, our cosmos could easily be such a system- even without ChaosMote's excellent statistical treatment, we can't be sure that, just because things in general continue to happen, an event like the big bang could happen an infinite number of times. No matter how wide the scope of your analysis, it may be that the 'final answer' is that we are indeed working within a single time-dependent system.

I think that the most reasonable thing to assume is that every possible kind of reality exists. Why? Well, there seems to be no good reason for it not to. To assume that the universe is the sole reality is one assumption too many for me, and I say the fewer assumptions there are, the better.

If I'm not mistaken, this is the strong assumption underlying the whole post. And I would encourage you to consider this claim in probabilistic terms, rather than just working within a believe/disbelieve binary. What is your degree of confidence in this proposition, and why?