Inside the Schrodinger's cat's box, the moment the radiation is detected by the counter, doesn't this mean the system already has a fixed eigenstate (a collapsed wave function, or is decoherent, whatever you like to call it)?
At the end of your question, you give a list of things that might have happened to the system, and treat them as equivalent, but they are not equivalent. Decoherence is a well-understood process that suppresses interference between different versions of a system after the different versions have a differential effect on other systems.
For example, the different versions of the cat in this experiment interact with the box, the geiger counter and possibly other stuff. A live cat and a dead cat may be distinguished in many different ways, e.g. - the dead cat doesn't breathe and so doesn't make as much sound. So then the walls of the box and the geiger counter may vibrate differently if the cat dies: the box and the counter contain information about the cat. As a result of that sort of interaction and many others, different versions of the cat cannot undergo interference. To restore interference you would have to undo that information transfer so that nothing in the outside world contained that information about the cat. The key issue here is not whether the system that contains the information about the cat is macroscopic. Rather, the issue is whether some system other than the cat contains information about the cat. Whether that system is microscopic or macroscopic is irrelevant.
Now, in the particular example you gave, the cat will have interacted with geiger counter and the box and so on long before you open the box. The information from the geiger counter and the box will have been spread to other systems like the table the box is resting on, and it will have been spread to you. You won't know the outcome of whether the cat is dead, but the information will in general have had some small effect on the state of your body. So for any particular version of you the live or dead state of the cat will be fixed with some particular value. There will in general be multiple versions of you, but each one will be bound to see some particular outcome before the box is opened. This happens extremely rapidly by everyday standards according to papers about decoherence.
Now, why would people say that the outcome isn't fixed before you open the box? Quantum mechanics says that where there was only one version of the cat, and of you, before the experiment, there are multiple versions afterward. This means that judged from the perspective of the relative state before the measurement, the relative state after the measurement is unsharp. Now, any particular version of you will see only one outcome. As a result some people mistakenly concluded that the state changes in a way that violates quantum mechanical equations of motion and eliminates one of the possible states. Since there is no explanation of how this alleged process takes place, it is not possible to pin down when or where it happens. Some people say it only happens when a person looks at a measurement result. This is an anthropocentric and false way of understanding quantum mechanics.