I too find your views interesting and generally I would agree with the thrust of your post. I tend to reject using science to provide some sort of theological position (and I reject using science against theology proper). However much of current debate(s) seem to be an odd mixture of both science and theology, be it for or against.
I see the fine tuning argument as an inference, and I tend to view the constants as required to practice science (you may provide an alternate view if you wish). It is difficult to think, for example, of any chemistry without the charge of an electron set at what it is. I cannot see any probabilistic argument replacing that value (as one example of a constant).