The Grand Design

I've just finished "The Grand Design": Stephen Hawking's explanation of how the universe came to be. Chapter 7, 'The apparent miracle', addresses the problem of fine-tuning whereby many fundamental constants of the universe appear to be fine-tuned for life. This appearance of fine-tuning is a fairly widely accepted phenomena and demands explanation. But his explanation still leaves me wanting.
As most do, Hawking appeals to the anthropic principle, which for our purposes can be read as "of course it looks suitable for life, because if it didn't then we wouldn't be here asking questions". Now this only works if there are many universes. If there are countless universes with different parameters, then it seems reasonable that some might fluke the right parameters, and those are the ones that would have curious life forms. However if there is only one universe, then the incredible odds-against suggest that chance alone could not given us the right parameters. By analogy, it is not surprising that people win Lotto sometimes, given the number of games and people being played. But if in all of history there had only been a single player playing a single game of Lotto, then a jackpot result would have to be viewed with suspicion.
In chapter 7 he gives us the succinct: "We saw in Chapter 5 that our universe seems to be one of many, each with different laws.". Yet chapter 5 seems to do nothing of the sort. The closest we get is "The laws of M-theory therefore allow for different universes". In my mind it is a fairly substantial and unwarranted leap of logic from 'the universe could have different constants' to 'there exists oodles of universes with different constants'.
Typically, the home for all these universes is the multiverse. But there does not seem to be any good reason to think we can ever test for or prove the existence of a multiverse (and suggestions to the contrary are fairly hand-wavy), as it is by definition outside the realm of our observable universe. It seems that the usual motivation for invoking a multiverse is in order to enable the anthropic principle, thereby providing a naturalistic explanation for the apparent design we see in our universe. For example, Wikipedia gives us:

The concept of other universes has been proposed to explain why our universe seems to be fine-tuned for conscious life as we experience it.

However this is circular reasoning: in order to demonstrate that the universe has naturalistic causes, we had to invoke an untestable extra-natural multiverse that we only invented to solve the problems with a naturalistic causes.
Hawkins believes he escapes the problem of a multiverse by instead packing all of these universes as different possible histories of our own universe, in the freaky quantum 'everything possible history is happening at once' kind of sense (i.e. Feynman's sum of histories). The universe then collapses onto life-sustaining constants because we're observing it. But this still seems to suffer the same kind of problem: declaring that the universe could have had different constants and laws is very different to declaring that there are different histories that would take on all these possible combinations. I'd love to hear from someone who understands the physics better whether there is any valid explanation to bridge this gap.