Jaya Śrī Kṛṣṇa Ānanda-jī,
You are opening up a very complex issue. I am uncertain whether I can provide you with a total solution, but I may be able to point you in the right direction. Advaita-vāda is a term referring to the "non-dual doctrine." This and "acintya-bhedābheda-tattva" are summary phrases, something like a calling card for the structural modes, i.e., the default ontological modality by which any given philosophical issue is to be "framed." I will refrain from unpacking the term more, as you seem to have no particular issue there.
As far as Caitanya's particularly focused manner of Kṛṣṇa-Bhakti, it is important to recognize that, historically speaking, Viṣṇu represents the usual popular deity in South Asian religion. Among "Hindus," some 70% or so self-identify as Vaiṣṇavas, compared against the 24% or so of those who self-identify as Śaivas, or the 6% that identify as Śāktas or Neo-Hindus (for the latter, read, "eclectic Hindu"). This is according to the most recent polls that I have come across. This is because, historically, Viṣṇu heralds the earliest traditional version of Hindu thought. Most of the post-Vedic classics are Vaiṣṇava: considering the Purāṇas and Itihāsas alone, Vaiṣṇavism was the most prolific literary culture in South Asian antiquity after the Vedic-yajña materials. Much of this grew directly out of the Yajña science of the ancient Brāhmaṇas. If one simply compares literary materials among the various sects, Vaiṣṇavas are bar-none the premier historiographic school of South Asia. This is because Vaiṣṇavas were the initial Brāhmaṇical direction taken toward monotheism, and, it appears to me, arose from a Dravidian-style of Brāhmaṇism. Śaivism was, by comparison, a later, antinomian (cf., tantric) appendix to the Vedic cosmological pantheon. Its popularity grew from two directions: (1) Brāhmaṇas concerned to govern the dark powers of the universe, and (2) outcaste cultures of wild abandon who sought to integrate into or appropriate the prevailing religious tropes of normative Vedic-Vaiṣṇava culture.
Certainly, my experience has been that Westerners in particular tend to have a greater affection for antinomian versions of Indian religious thought, perhaps not least because of the emphasis on worldly freedoms, while Vaiṣṇava conservatism has tended to receive a more critical reception for its normative tendency to idealize a "clean-cut" or "puritan" hierarchy.
As far as truth-seeking is concerned, we feel compelled to ask which truths are being sought. Vaiṣṇavas of the Bhāgavata variety scorn the five liberations (which are, according to one reading, worldly), seeking only to act from a morality which places the Good of the world before the good of oneself. Gauḍīyas are perhaps best considered as physicians whose role in history is to break such arthritic conditions as prevent the incalculable swarms of sanātana-ātmans from losing their awareness of their essential connection (yoga) with Īśvara.
And of course, there are three (or four, if you count Śakti) primal deities in India: Brahmā, Viṣṇu, and Śiva. These are not simply "accidentally" primal, but represent the three phases of Time, past, present, and future.
However, Kṛṣṇa identifies himself not as the present, but as Kāla, as Time given as an historical whole. Thus, his self-understanding as avatārī is, at least within the traditional Vedic cosmo-ontology, the orignal axis of existence. This is an ontological matter which has been discussed at great length by not only Gauḍīyas, but among countless other lineages of Vaiṣṇavas, Śaivas, Śāktas, and even Buddhists (Bauddhas). What we actually see, historically, is that this view has been tremendously influential among Asians, even if it has not always been described explicitly in these terms. Indeed, the Śaivas, Śāktas, and Bauddhas most significant response has been to "emulate" the Vaiṣṇavas on this matter, by reinscribing their own deities (iṣṭa-devatāḥ) as all-encompassing forms of Time (indeed, this is most likely why Śakti takes the name "Kālī," a term which is the feminine nominal stem of "Kāla," and why Śiva-Rūdra later becomes "Mahākāla," from whom the Kāla-cakra-tantra takes its name). What is significant for most Hindus is that one is original, the other a derivative. And this tradition remains influential just in its original form, not because of some historical accident, but because the original thought revealed by Kṛṣṇa in the Bhagavad-Gītā is itself quite powerful. As Kāla, Kṛṣṇa is the Primordial power that moves the whole of world from its origins to its fate. A rose by any other name is still a rose. That Kṛṣṇa woke the world up to the event we call "History" is not something we can easily challenge. Nothing has been the same since.