I think Sri Nityananda is the original Guru for those in His parivar. For those in Adwaita parivar, Sri Adwaita Prabhu is their orginal Guru. For those in Gadadhara parivar it would be Sri Gadadhara Pandit. Adwaitaji, is that correct?
I think this concept arose because the Gaudiya Math uses as a resource the writings of Bhaktivinoda Thakur, who is in the Nityananda parivar. The Gaudiya Math, however, cannot make this same claim because of the lack of diksa connection.
There is the concept of Samasti Guru and Vyasti Guru. The Samasti Guru is the aggregate of all Gurus from wherein the power of Guru (guru shakti) descends onto this world in the person of the local Guru in this world, ie. the diksa and siksa Guru. There is also mention of the Sravana Guru in the commentaries of Ananta Das Pandit in Madhurya Kadambini. This is the devotee person from whom one prior to diksa hears about bhakti topics. The Samasti Guru is a form of the Lord.
I never gave the idea of adi-guru a second thought, but now that you brought it up, indeed I wonder where it came from. Bhagavata (10.16.26) and Brahma Samhita (27) speak of Krishna as the adi-guru. I looked up Caitanya Bhagavata (5th chapter), which narrates the Vyasa-puja ceremony of Nityananda, arranged by Mahaprabhu and others in the house of Srivas Pandit, but there was no reference to his being Adi-guru.
The division of diksa, siksa and sravana-gurus comes originally from Bhakti-sandarbha, as do the concepts of samasti and vyasti-guru. There may be sravana-gurus after diksa as well. The difference between siksa-guru and sravana-guru is that one makes a permanent bond with the siksa-guru, while any senior Vaishnava may act as sravana-guru on occasion.
The origin of the concept of vartma-pradarsaka-guru is a mystery. I have never managed to track down its first appearance.
QUOTE
samsarera para haiya bhaktira sagare
ye dubibe se bhajuka nitai candere
amara prabhura prabhu sri gaurasundara
e bada bharasa citte dhari nirantara
(Caitanya Bhagavata 1.17.152-153)
This statement is extremely subjective and is not a general rule for all Vaishnavas. Vrindavan das had greater love of Nitai than of Gaura, viz. amar prabhur prabhu sri gaurasundara - "Sri Gaurasundara is the master of my master (Nitai)." A type of bhavollasa rati in Gaura lila. Similar feelings are uttered by Ishan Nagara about Advaita Prabhu in his Advaita Prakash. It does not mean that Nityananda is the adi guru of ALL Gaudiya Vaishnavas.
QUOTE
The origin of the concept of vartma-pradarsaka-guru is a mystery. I have never managed to track down its first appearance.
kimva vartmoddesha gurur mantra guruh siksagurur iti gurutraye.....(Saranga Rangada tika of Krishna Karnamrita verse 1)
The archetypal vartma pradarshak guru is the courtisane Cintamani, who did nothing else but bringing Bilvamangal on the path of Krishna bhakti.
QUOTE
The division of diksa, siksa and sravana-gurus comes originally from Bhakti-sandarbha, as do the concepts of samasti and vyasti-guru.
Indeed, Rupa and Sanatan Gosvami can be rightly called eka guru vadis, for the verses they quoted on Guru in their main granthas Bhakti Rasamrita Sindhu and Haribhakti Vilasa all put Guru in singular case. It was Kaviraja and Jiva that split Guru up in diksa, siksa and vartmoddesha.