that's fair. I guess a simpler way of saying that I'm getting at here is: "I don't understand your distinction between task and means based on the examples you provided." That's why I said that definitions would be helpful. Perhaps more examples would also be helpful. We're already butting up against category theory here so it's fine to say "these are exemplar-based categories" but in that case my complaint boils down to "I don't understand which salient features of your examples should be used to categorize things as being closer or further from your exemplars."
I do think that a task/means distinction is possible, I'm just not sure what you mean when you make that distinction.
Trying to define those axes in the way that makes the most sense to me would be something like:
The task axis is concerned with the material/sensory inputs and goals of a behavior, while the means axis is concerned with the process used to pursue some goals given some inputs. The attainment axis relates to the specific measurement techniques and the results of using those techniques. The task/means parts of a definition may constrain what kinds of measurement are seen as accurately measuring achievement for a specific behavior vs. measuring confounding information attributable to multiple distinct behaviors.
But these definitions don't line up with your exemplars as I pointed out above.