This is a very promising approach but I would look at it a bit differently.
First, it seems that there are really two questions here. The first is
why the parameters of the universe are what we observe. Theoretically
we can measure the actual values of the parameters to extremely high
(arbitrary?) precision as technology advances. Hence the information
content in these parameters may turn out to be very high.
The second question is why these parameters happened to fall into the
range that would allow the formation of life. This is a narrow range
but still it will have less information content then the actual parameters
which are somewhere within that range.
These two questions seem to be largely independent, and the second is
what I was trying to address.
I think what you need to do is to come up with different theories that
predict the creation of the universe in a form which can allow life.
Then you can compare the information content of the theories to see which
is simplest. But "the parameters of the single universe are chosen
randomly" is not a valid contending theory because it does not predict
the existence of life with any significant probability.
I'm not sure how to take into account the fact that different models
may allow for the creation of life only with some probability. My
preference would be to consider models in which the creation of life
is a certainty. Then you are comparing apples to apples when you count
the size of the theory.
Two possible theories, as I mentioned, are first that you create all
possible universes with all different variations on the parameters
we observe. This is probably a pretty simple theory. The other is
that you create some kind of primordial universe, maybe very different
in nature from our own, possibly mathematical in form, but such that
intelligent life can evolve. Then that intelligent life will naturally
create simulations or baby universes which explore all different kinds
of physics, including structured ones like ours with matter, space,
distance, time, dimensions, etc., concepts which may be absent from their
own universe. Conceivably this could also be an extremely simple theory.
We really don't know nearly enough at this point to know what theory is
going to be the simplest.