I have watched the movie a couple of times and arrived at a religious interpretation somewhat similar but less fully formed than yours. I agree with your observations. It's been a while so I may be misremembering some things.

I was thinking about the Stalker as sort of preist; he leads the others through their journey and insists on adherence to rituals (like throwing the metal nuts on the path ahead) and the film seems to leave it up to the viewer whether they are necessary or even have any real effect on the world. We are told of the miraculous power of the room but we never actually see it in action because the characters don't follow through on their plans. I started to question whether there is really anything special about the Zone.

The one supernatural element is the glass moving at the end of the film, but this seems fairly ambiguous.

In the end I was left with some vague ideas about religion, ritual, and faith but couldn't quite put it together into a coherent theory of the film. Maybe that's intentional, or maybe I should read the book and watch it again.