So .. a superposition of states would really just be a point in time during which the state variable takes no specific value?

Or, it isn't so much that Schrodinger's famous cat is both alive and dead at the same time, as that it's neither?

The thing about the cat in the box is that, when you later open the box, it's some kind of cat that's revealed. You don't open the box to find a nice loaf of bread. I.e., seems like something must have some kind of state, in that box, when no one is looking, that retains at least the possible outcomes and precludes others.