A different storyform would create a different story, though one could dress it up to look similar.
However, I do not think it would be necessary to use a different storyform to reach those ends. The example storyform for Hamlet has one story point that could make the difference depending on how it is interpreted and illustrated by the author. The Benchmark for the Main Character throughline is Changing One's Nature. A benchmark indicates the progress through the development of a particular throughline. One could choose to emphasize Hamlet's transformation into some other psychological way of thinking (crazy or otherwise) by emphasizing the MC Benchmark.
Additionally, the Signposts for the MC throughline are as follows and give more areas to play up or play down the crazy card:
- Developing a Plan (Figuring out how to deal with one's father's death)
- Playing a Role (Pretending to be crazy)
- Changing One's Nature (Slowly changing into the character one pretends to be)
- Conceiving an Idea (Coming up with the idea that one's fate is in the hands of Providence)
As you can see, it is set up to easily be one way or the other, depending on how you illustrate "Changing One's Nature" in the context of the story. One could equally interpret that as going from playing crazy to being crazy, as well as going from passive to active, or growing up, or anything that fits within the broad context of "Becoming" someone/something.