So... how do cosmologists (Hawking in particular, because you keep citing him) feel about the universe being "designed"? You examine the first two explanations, and discover that scientists don't seem to like either very much. Okay. But when we're talking about "best" (or, as I'd refer to call it in this case, "least bad"), we need to examine
all of the options. After all, if our options are A, B, and C, and A has a probability of 1:10^20 and B has a probability of 1:10^30, we do not get to conclude that C is the most likely option without examining it. C could have a probabilty of 1:10^4, or a probability of 1:10^40*.
And the fact of the matter is that the option you want to offer as the "best explanation" is
not even considered an explanation. It's not considered a valid explanation for why the universe is the way it is, any more than it is considered a valid explanation for why we see such diversity of life on the planet. It might technically be possible. It's also unscientific, unfalsifiable, and fundamentally useless. I mean, Hawking, the scientist you are basing most of your citations on, quite obviously doesn't think that design is the most reasonable answer - he's an atheist. He wrote an entire book attacking this argument. In fact, reading an excerpt published in the
Wall Street Journal, it seems that he in fact endorses the "chance" option, and the multi-universe hypothesis:
Again, we run into exactly the same problem as the cosmological argument. You appeal heavily to very complex theoretical physics that basically require a post-grad course just to understand the mathematics involved, but the scientists just keep not following through to your conclusion for some reason. If your argument for the existence of god depends on cosmology and something like 80% of cosmologists are atheists, you've got a honkin' big problem.
...Yes, and this is why "supernatural design" belongs in a bin. It has no explanatory power or scope, its plausibility is incalculable, and it is not falsifiable. It, like all supernatural explanations, makes no testable predictions and as a result is completely worthless.
*If they were a mutually exclusive, complete set of options, then yes, P(C) would necessarily be P(U) - P(A) - P(B), but this is part of why I find the trichotomy so problematic here. Neither of the two naturalistic options are universally accepted, and the supernaturalistic one is by definition useless.