Fine tuning argument assessed

[hatsoff]

In the discussions I can recall (and the beliefs I held when I was a theist), the argument from fine-tuning is that life would be impossible unless those values were in a very tight range, and that any deviation would make life impossible.

That's not exactly it, no. The argument aims to show that on naturalism, the life-permitting range of values is relatively small. Obviously, there are many more possibilities once we look at the supernatural. And that's one of the things the theist wants us to do---start looking at options other than naturalism.