Maharajji answers questions in the Śrī Guru Darśanam, pp. 99-100.
Question: What is the meaning of the mahā-mantra? What should be the mood of prayer?
Answer : The mahā-mantra has three names: Hare, Krṣṇa and Rāma, which are by nature an invocation. Invocation, in this case, means to call somebody out of love and affection. And when you call with great affection, you repeat it. [..] It is just the calling of Krṣṇa in an affectionate mood- the mood of the residents of Vraja, when there is an affectionate relationship with Bhagavān. You call Him in that affectionate relation.
Question: So it is not Harā (Rādhā) or something like that?
Answer: If you take the meaning Harā, then it is not vraja-bhakti. Vraja-bhakti or rāgānugā-bhakti, means following the footsteps of the great ācāryas. They, including Mahāprabhu Himself, chanted it as Hari, not Harā.
When people want to imitate, they want to perform better than the original. You can chant any name, as there is no restriction. You can chant whatever name of Bhagavān you like, but vraja-bhakti means following in the footsteps, especially of Sri Caitanya Himself. Mahāprabhu was in the mood of Srimati Rādhā. He is not going to chant Her name. He is calling Krṣṇa, as Rādhā calls Krṣṇa. All these are names of Krṣṇa.
The basic principle of uttamā-bhakti is that Bhagavān is in the heart of the devotee and the devotee is in the heart of Bhagavān. They are related to each other in a loving relationship. There is Rādhā and there is Krṣṇa. Krṣṇa is Bhagavān and Rādhā is the devotee. The mood in which Rādhā calls Krṣṇa is a loving relationship- that is the mahā-mantra, and then to follow in Her footsteps, that is rāgānugā-bhakti.
There are many explanations of the mahā-mantra, because in Sanskrit, it is possible to attribute many different meanings. But what was the meaning in the mind of Caitanya Mahāprabhu? That is what we have to follow, not that we get carried away with some fantastic meanings.
Question: And the name Rāma in the mahā-mantra is also Krṣṇa, not Balarāma?
Answer: It is only Krṣṇa. It is neither Balarāma nor Paraśurāma nor Rāma, the son of Daśaratha. It is Krṣṇa. Krṣṇa is Rāma.