Quote Originally Posted by grafrich View Post
1st one: I didn't phone during the time that I was supposed to. That time has gone, therefore the action I performed was 'not phoning', which I completed successfully.
I don't think so. It is not about successfully completed 'not phoning'.
The perfective here is used in its usual meaning 'single action', 'action as a whole', action that has no significant time duration. We are just saying that this single action was not performed.

Quote Originally Posted by grafrich View Post
Я не позвонила
Я не звонила

How would you explain these 2 example sentences in terms of choice of aspect?
In my opinion, the choise of aspect is rather arbitrary in this particular example.
'Я не позвонила' - I didn’t perform the action of phoning.
'Я не звонила' - I didn’t phone. (I had a chance to phone but I never phoned.)
Aspect here does not tell us any essential information, and the grammar does not force the specific one to be used either, so both can be used:

- Ты звонила заказчику?
- Я не звонила. / Я звонила.

- Ты позвонила заказчику?
- Я не позвонила. / Я позвонила.

Quote Originally Posted by grafrich View Post
I failed to phone.
It should be дозвониться:
Я не дозвонилась.
Я не смогла дозвониться.
Мне не удалось дозвониться.