Devotee: I am not aware of any aspect of Gauḍīya siddhānta which relies on this, (on the point of the divinity of Śrī Caitanya Mahāprabhu) and I am thinking of Gauḍīya siddhānta in terms of ārādhyo bhagavān vrajeśa-tanayas tad-dhāma vṛndāvanam. Please set me straight on this.

Narasiṅgha Mahārāja: Yes, that is Mahāprabhu’s conception contained in the verse by Śrīnātha Cakravartī Ṭhākura;

ārādhyo bhagavān vrajeśa-tanayas tad-dhāma vṛṇdāvanaṁ
ramyā kācid upāsanā vraja-vadhū-vargeṇā yā kalpitā
śrīmad-bhāgavataṁ pramāṇam amalaṁ premā pum-artho mahān
śrī-caitanya-mahāprabhor matam idaṁ tatrādaro naḥ paraḥ

“The Supreme Personality of Godhead, Lord Kṛṣṇa, the son of Nanda Mahārāja, is worshipped along with His transcendental abode Vṛndāvana. The most pleasing form of worship for the Lord is that which was performed by the gopīs of Vṛndāvana. Śrīmad Bhāgavatam is the spotless authority on everything and pure love of Godhead is the ultimate goal of life for all men. These statements, for which we have the highest regard, are the opinion of Śrī Caitanya Mahāprabhu.” (Caitanya-matta-mañjuṣa by Śrīnātha Cakravartī Ṭhākura)

But we find adjustment in the conception of Mahāprabhu’s devotees, in that the devotees feel that their only approach to Vṛndāvana, to Bhāgavata, to prema–bhakti, to gopī-bhāva, is via the lotus feet of Śrī Caitanya.

A Gauḍīya Vaiṣṇava feels and thinks that his only hope in approaching Rādhā-Kṛṣṇa is by surrender to the lotus feet of Guru and Gaurāṅga. Surrender, śaraṇāgati, slavery to the infinite is the highest freedom. This principle has been accepted as essential by all Gauḍīya Vaiṣṇavas. Gaurāṅga is the infinite. See how strongly Kṛṣṇa Dāsa Kavirāja Gosvāmī speaks in this regard:

hena kṛpāmaya caitanya nā bhaje yei jana
sarvottama ha-ileo tāre asure gaṇana

“One who does not show respect unto this merciful Lord, Śrī Caitanya, or does not worship Him should be considered a demon, even if he is very exalted in human society.” (Cc. Ādi-līlā Ch8.12)

Actually the highest prema in kṛṣṇa-līlā is found in the mādhurya-līlā but categorically higher than the mādhurya-līlā is the audarya-līlā, that is the wholesale distribution of the mādhurya-prema. This mādhurya-prema finds its highest expression in Śrīmatī Rādhārāṇī whose essential nature is mahā-bhāva. Gaura-līlā is that audarya-līlā, the wholesale distribution of kṛṣṇa-prema. To the degree that we surrender to the lotus feet of Gaurāṅga, to that extent we will find ourselves in Vṛndāvana, all things provided. In Vṛndāvana the highest position is not held by Kṛṣṇa but by Rādhārāṇī. The prayojana–tattva of the Gauḍīya school is to engage in Her service. Śrī Gaurāṅga is the sole access to that plane of service.

yathā yathā gaura-padāravinde
vindeta bhaktiṁ kṛta-puṇya-rāśiḥ
tathā tathotsarpati hṛdy akasmāt
rādhā-padāmbhoja-sudhāṁbu-rāśiḥ

“One who is extremely fortunate may get the mercy of Lord Caitanya. As much as one can devote his full attention to the lotus feet of Śrī Caitanya, to that extent he will be able to taste the nectarine service of the lotus feet of Śrīmatī Rādhārāṇī in Vṛndāvana. The more one engages in the service of Śrī Caitanya, the more one finds oneself in Vṛndāvana, tasting the nectar of the service of Śrī Rādhā.” (Caitanya Candrāmṛta 88)

Pure devotion to Gaurāṅga is best of all. Those who neglect to take shelter of Śrī Gaurāṅga are in essence destroying themselves.

kriyāsaktān dig dig vikaṭatapaso dhik ca yāmenā
dhigastu brahmāhaṁ vadana-pariphullān jaḍamatīn
kimetān āmo viṣaya-rasa-mattān-narapaśūn
na keṣāñcil-leśo’py ahaha milito gaura-madhunaḥ

“Woe to the smarta-brāhmaṇas, who blindly follow the Vedic rituals! To hell with those who unnecessarily practice harsh penance’s. Woe to those who try to control the mind and senses by following the eight-fold yoga system. Woe to those who artificially practice brahmacarya and imagine that they have become liberated simply by saying aham brahma’smi, “I am God”. Woe to those whose voices are filled with flowery words of dry speculation. They are intoxicated by the taste of mundane pleasure.  Why should we lament for these animals in the guise of men? We lament because, alas—they have not tasted even a tiny drop of the nectar from the lotus feet of Lord Gaurāṅga.” (Caitanya Candrāmṛta 32)

Without devotion to Gaurāṅga one’s knowledge of scripture is foolish nonsense.

caitanyam idaṁ viśvaṁ yadi caitanyam īśvaram
na viduḥ sarva-śāstra-jñā hy api bhrāmyanti te janāḥ

“Great scholars of the scriptures who do not accept Lord Gaurāṅga, as the Supreme Personality of Godhead, are forced to wander aimlessly throughout this universe of dead matter. Their so-called knowledge of the scriptures will be useless to them. Birth after birth, they will wander from one planet to the next propelled by their pious and impious acts.” (Caitanya Candrāmṛta 37)

Higher than Gaurāṅga are Gaurāṅga’s devotees.

āvad-brahma-kathā vimukti-padavī tāvan na tiktī-bhavet
tāvac-cāpi viśṛokhalatvamayate no loka-veda-sthitiḥ
tāvac-chāstra-vidāṁ mithaḥ kalakalo nānā-bahir-vartmastu
śrī-caitanya-padāmbuja-priyajano yāvan na dṛg gocaraḥ

“As long as one has not seen a pure devotee of Śrī Gaurāṅga, he will be engaged in tasting bitter talks about the impersonal path of liberation. As long as one has not seen a devotee of Lord Gaurāṅga, he will be bound by social and Vedic convention, blindly following formalities and traditions without understanding their purpose. As long as one never sees one of the bee-like devotees addicted to drinking the nectar from the lotus feet of Śrī Gaurāṅga, he will be forced to walk in endless circles on the labyrinthine paths of dry Vedic scholarship, wasting valuable time in useless discussions on futile religious practices.” (Caitanya Candrāmṛta 19)