Dear Lawrence, I am following your good idea to double the comment.
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Dear Lawrence,
Thank you so much for your generous compliments to our essay. As you see, we are showing there how Tegmark's MUH is refuted on the scientific ground. Yes, it goes against the dominating opinion of the community of cosmologists (and your own), that the full-blown MUH is unfalsifiable, but our refutation looks very solid for me.
About your 'couple of points'. First, your distinction of WAP and SAP fully agree with the conventional one, as I may judge. It isn't clear to me what point you were trying to make about them. Second, we use the word "chaos" in its ancient meaning, as we stress it when this word is used the first time, pointing there to Platonic philosophy. This meaning sometimes is expressed by such words as "nothingness" or "nothing". This formless entity, chaos/nothingness, is a source of pure accidental, random, causeless factors. It has little to do with the mathematical concept of "dynamical chaos" you mention, which assumes certain mathematical forms already given.
Your ideas about "the soul of mathematics" sound very interesting to me, and I would very much wish to discuss them with you in much more detail than this specific place and occasion allows. You know how to find my email. Please be assured that I would highly value communication with you on these and other questions.
All the best,
Alexey.