Absolutely, I agree in all respects. (Though, I fear I already have a hard time being understood in English, so if I started mixing Greek into my prose, it'd be hopeless...)

One quick note for future reference is that the second kind of love is φιλία ("friendship") rather than φιλαδελφία (φιλία-ἀδελφός "the love of brothers"). It is common to address someone as "ὦ φίλαι," "my friend" or "my dear."