Usage of find

There are the common-known classification about dynamic verb class.
It's about meaning-based categorization and the subclass 'achievement verb' is one of them.
The verb 'find' is among the achievement verb class,as I found.
It is also suggested that when the progressive is adopted with achievement verbs there can be 3 possible interpretations.
Each of them is iteration, inception of an event and stretching out the moment to emphasize on the action.
i.e. He is nodding his head in agreement / Kim is realizing his mistake / He is dying of cancer.

Then it seems legit to assume the verb 'find' can be with progressive aspect and the way of its meaning's being interpreted is apparently among 3 of them.
But I also now come across this example with the indication of mark showing falsity.
* I am finding my key. (esp, the context is given to contrast it with 'I am looking for my key')

Still, there are many more examples such like,
e.g. He is finding every possible tangent to solve the problem
Each team is finding its own way to tackle the problem.

In sum, one can surely guess that there is some subtle difference between 'find' and any other achievement verbs.
What is your way of judging when it is acceptable or when it is not concerning the usage of 'find' with progressive?

And what do you think about 'find' as an achievement verb, which seems to be distinguised from other ahcievement verbs?