I strongly favor the "future theory" thing.
Thinking that the nature of natural constants is just
a random incident shows rather that it is not explanable
currently why it is so. Not that they are really random combintions.

Before Newtons theory of physics, one might say, that
all these strange mechanical behaviours might also be
"random laws", and it might be an anthrophic princile that we
see them this way.
But with the knowledge of mechanincs we can explain all
these (everyday scale) phenomenon by simple mechanical laws.
The same goes for the movement of stars/planets before
the knowledge of Keplers laws.

I rather think that there is a simple, yet unknow
"theory of everything" (Weltformel).
And all these physical constants can be derived from it.
And that there are/where no other combinations of it.

Take this mind-game:

Even if there where a universe with different
natural constants, take any combination (like strength of
graviation)

No matter what combination, one think would be allways the
same:

The logic of mathematics!
1+1=2 will allways be the same, in any "combination" universe. (and more complex equasions of course)

I think that this constancy is a proof of
"the one main formula"

BTW, if there where a god, he would not
have the power to change everything, as he could not
change principle logics/mathematics.