I don't think we need to show that an alternative universe to provide support for the values of our physical constants and how things can be different if they change so that it will affect the production of life being created. Though I find it ironic that you say my argument would be meaningless when multiverses are taken seriously by mainstream scientists as being a reality.
We don't need to demonstrate an alternative universe for the fine tuning argument. IN fact an alternative universe would invalidate fine tuning as it introduces a multiverse. We can measure the current physical constants in our universe and also calculate what slight variations to those variations will produce. This shows how our physical constants need to be fine tuned. The science used for this is the same science we have used for our well known theories the Standard Model. The physical constants for the basis of all our theoretical equations of physics. AS this article states
Accurate evaluation of these constants is essential in order to check the correctness of the theories and to allow useful applications to be made on the basis of those theories.
Physical constant
An example of how we can measure constants with the same science that our fundamental theories are based on and to measure any variation and its effects are found in this article below.
The fine-tuning of the universe for intelligent life has received a great deal of attention in recent years, both in the philosophical and scientific literature. The claim is that in the space of possible physical laws, parameters and initial conditions, the set that permits the evolution of intelligent life is very small. I present here a review of the scientific literature, outlining cases of fine-tuning in the classic works of Carter, Carr and Rees, and Barrow and Tipler, as well as more recent work.
We will touch on such issues as the logical necessity of the laws of nature; objectivity, invariance and symmetry; theoretical physics and possible universes; entropy in cosmology; cosmic inflation and initial conditions; galaxy formation; the cosmological constant; stars and their formation; the properties of elementary particles and their effect on chemistry and the macroscopic world; the origin of mass; grand unified theories; and the dimensionality of space and time. I also provide an assessment of the multiverse, noting the significant challenges that it must face. I do not attempt to defend any conclusion based on the fine-tuning of the universe for intelligent life.
http://www.publish.csiro.au/AS/pdf/AS12015
Another example of how we can measure the physical constants and how they are tied to ouur current theories is the cosmological constant. Dark energy is now an important part of our understanding of the universe. Yet as Leonard Susskind says
"The great mystery is not why there is dark energy. The great mystery is why there is so little of it [10−122]... The fact that we are just on the knife edge of existence, [that] if dark energy were very much bigger we wouldn’t be here, that's the mystery." A slightly larger quantity of dark energy, or a slightly larger value of the cosmological constant would have caused space to expand rapidly enough that galaxies would not form.
So the same methods used to calculate the amount of dark energy needed to support our galaxies and fundamental theories like relativity is also used to determine the fine tuning of our universe for life.
Just Six Numbers: The Deep Forces that Shape the Universe by Martin Rees – review
The astronomer royal addresses the cosmic coincidence that six numbers in physics are just right for the emergence of galaxies, stars, chemistry and people
Just Six Numbers: The Deep Forces that Shape the Universe by Martin Rees – review | Tim Radford | Science Book Club