There are several questions to be reflected upon here.
While there is merit in speculating that there is some kind of a conflict between Angirasas and Bhrigus it cannot be characterised as Indra vs Varuna.
Varuna is the primary Devata of Rta (Rtasya Gopa) all Devatas are Rta Palakas in different ways. Thus, Indra is responsible for all of that. With Angirasas being the primary Rshis of Rigveda making them a part of Indra vs Varuna conflict completely contradicts the perspective of RgVeda itself.
Secondly, If Bhrigus are the distinguished Drashtaras of Atharva Veda (which they are), then that represents a higher order material dimension. So the conflict if any is in the realm of the composition of spiritual-material and not excellence vs order. Order is the fundamental concern of Rgveda itself through Rta. RgVeda is fundamentally about Devatas as Rta Paalakas with Varuna representing Daiveeka excellence in the substratum and all other Devatas representing excellence in specific aspects with Indra has been the Paalaka of everything.
So making this a conflict between Order and Excellence represented by Bhrigus and Angirasas would be technically incorrect. If Angirasas praised Rta as much then they are equally upholders of Order. I guess the difference was what Order meant and not Order vs Excellence.
Further, if Bhrigus were the reshapers of Mahabharata in the way the post explains then why so many verses in Mahabharata uphold Trayee and not mention Atharva in parts considered beyond Jaya? There are equal references to all four Vedas and Trayee alone in MB in different places.
Even further, what explains expositions about Moksha (Mokshadharma Parva) and its enormous impact on India subsequently with many traditions emerging? This dimension itself is absent in Avesta and could not have been a Bhrigu 'innovation' alone, if that were the case we would have seen it in Avesta - if the narrative in the original post were true.
We are missing the point why Mahabharata is Vyaasa rachita. Shuka is the son of Vyaasa. Shuka is the greatest representative of Moksha. In a part, that was elaborated by Bhrigus for their glory, if that were true, why would they make Shuka a son of Vyaasa and not a Bhrigu? Why would they miss out on such an opportunity? There is a huge metaphor out there in Shuka being Vyaasa's son.
Beyond all this, we are reading Mahabharata in isolation. It is deeply connected with all Puranas and Bhrigus are not as much present in other Puranas as they are in MB except, of course, Shaunaka Maharshi (Bhrigu) being the leader of the audience and Souti being the the narrator. We are totally missing that there is a Vasistha dimension to Mahabharata. We are also missing that Mahabharata is a whole restatement of the Adhidaivika plane presented poetically, mystically, metaphorically by RgVeda. What was accessible only by a ritualistic Tapasya was made so by Mahabharata purely on the literary plane to a good extent.
The strength of Mahabharata is that it can be read with any lens. That is its weakness too, we can read it with a reduced one either, until somebody holds the bigger one.
If one accepts this conflict theory alone, its amazing that somebody who were completely out of the original Drashta zone, came to sideline the pioneers and restated the entire Drishti on a wholly different plane that has since shaped life as much in the vision of the original. If that is so, let us hail such conflicts.
General editor of the BORI critical edition of the Mbh, V.S. Sukthankar, in his 1936 paper 'Bhṛgus and the Bhārata' made the bold claim that the group of rishis responsible for expanding the Mbh from an ancient war ballad of a Kuru war into this complex epic with subplots, morals, lessons, bhakti, and so on were the Bhṛgus.
Unbeknownst to most, the Bhārgavas seem to be rival groups (generally speaking) to the Angirasas. The Angirasa rishis primarily composed the Rgved, Yajurved, and Samved (the original trayi), while the contribution of the Bhārgava rishis peaks in the Atharvaveda (historically called the Bhārgavāngirasa veda).
While the Angirasas were devout Indra bhakts, the Bhṛgus worshipped primarily Lord Varuna (Asura Varuna), who stood in stark contrast to Indra. One demands excellence, the other demands order.
As per texts, Varuna is the sovereign asura par excellence, the same figure who survives in Iran as Ahura Mazda, the keeper of cosmic order. Indra, the fort-smashing warrior, takes the opposite path and is demonized into a daēva in Zoroastrianism.
The Bhṛgus also largely become the later day Vishnu bhakts. They apply traits reserved for Varuna, oceanic symbology, blue skin, the cosmic judge and sovereign, onto Vishnu, who in the Rigved is described primarily in his Vamana form.
Therefore, the Mahabharata, while being a beautiful text full of great knowledge and wisdom, was also a political coup, one in which the Bhārgavas reshaped the old Kuru war ballad into a vast dharma text. It was a systematic engineering to domesticate Arya Dharma into modern day Hinduism. I am not saying that the change was bad, I am saying it was less organic.
The Bhṛgus, largely absent from the core Vedic texts, through beautifully retold stories injected into our Puranic and Itihasa texts, ensured that their gods and ancestors finally prevailed, while all others were reduced to demigods or mere posts.
Well played, Bhrgus.