It takes one kind of craftsmanship to make a compelling story, and another to make an engaging game. It takes a third kind to align those two elements up against the border between fiction and metagame, so that they form two halves of a whole.
I think there is an inherit conflict between the game part and the story, and that in order to make the player become part of the story, one has to lessen the gaminess. And this is pretty much one of the main stuff of notgames.
I get at what you mean, that (as Michael also said), different people will have different thoughts on what kind of things feel right to do in a certain situations. Again, with the shooting-wolf example, the player might not think the loved one is worth saving and hence does not feel the same way the protagonist does and fail to sympathize and feel immersed. However, I would like to say that this is a problem between interaction and story, not between game and story. I actually feel that the game part is a detracting force that pulls away from the story and even immersion to some degree. So if you want to increase the "frama", I think that you need to think of it less as a game and instead as creating interaction that the player feels part of.
Now the problem of making player feel part of the interaction is very interesting, but as I said above, I would argue that it is a problem to try and fit in a game into it as well. To get the best possible story and player immersion, I think one has to disregard game elements and only focus on creating an experience. Of course game elements can still be very useful, but they should come from the wish to tell story and not be a base to build from.
Is your goal to tell the best possible story, or to blend story and game in the best possible way? Because I think the two are quite different problems.