First, to deal with the Vrishbha incident, the first thing to realise is that the form of Vishnu involved is Mohinī, since the text starts talking about her with no sign of stopping. While a later verse is usually translated as her having sex with the damsels, it actually uses the instrumental case. Thus, it makes sense for Mohinī to be possessing the damsels instead.
- Viṣṇu, the most excellent of those who wield Māyā assuming the form of a woman Mohinī deluded the Asuras and made the gods drink it.
Fascinated by the Cupid’s arrows Viṣṇu attained highest pleasure only there. He began to indulge in sexual dalliance with those women of exquisite beauty.
This makes sense with the story, as it explains why takes longer to recognize Shiva, as she could be sleeping letting the possessed damsels work mostly to themselves. Also, the story clearly has Mohinī's Maya and Shiva's Maya be the same thing.
Viṣṇu, the most excellent of those who wield Māyā assuming the form of a woman Mohinī deluded the Asuras and made the gods drink it.
The leading Daityas approached her and said—“Make us drink this nectar. Let there be no break in the lines.”
All those Daityas and Dānavas deluded by Śiva’s Māyā said thus and gave the nectar to Viṣṇu in disguise.
Both for that incident and more generally, not all forms of Vishnu are supreme. Some are partial, for example, Prithu
Brahmá recognised a portion of that divinity in Prithu
This is also recorded in his presumably different birth in the Devi Bhagavatam
Kâkutstha had the son Prithu, of mighty prowess. Prithu was the part incarnation personified of Visnu, and worshipper of the feet of the Supreme S'akti
Thus, it was probably one of them, especially all the Puranas not labeled Sattva in the Padma Purana tend to be ambiguous of which incarnation they are talking about.
As a side note, while we cannot say for sure Prithu has flaws (or close to flaws), there is the possibility he is the same as the Vasu Prithu, who steals a cow. It is mentioned in the Devi Bhagavatam and Mahabharata
Prithu and others, one Vasu Dyau's wife seeing Nandini, the sacrificial cow (Kâmadhenu) of Vas'istha asked her husband :-- “Whose is this excellent cow that I see? Vasu then replied as follows :-- “ O Beautiful one! This is Vas'istha's cow. Whoever, be he a man or woman drinks her milk gets his longevity extended to ten thousand years and his youth never ends.” Hearing this, the Vasu's wife said :-- “There is a very beautiful comrade (Sakhî) of mine, the daughter of the Rajarsî-Us'îna in the world, of auspicious qualities. O Mahâbhâga! Kindly bring to me from Vas'istha's hermitage that auspicious sacrificial milch cow Nandini together with her calf that yields all desires; my Sakhî will then drink her milk and be thereby free from disease, old age and become the chief amongst all mankind. Hearing thus, his wife's word, the Vasu Dyau, though sinless, stole away together with Prithu and the other Vasus the cow Nandini in utter defiance to the self-controlled Muni Vas'istha. When the cow Nandini had been stolen, the great ascetic Vas'istha came quickly to the hermitage with abundance of fruits.
On hearing these words of his wife, Dyu, moved by the desire of humouring her, stole that cow, aided by his brothers Prithu and the others. Indeed, Dyu, commanded by his lotus-eyed wife, did her bidding, forgetting at the moment the high ascetic merits of the Rishi who owned her. He did not think at the time that he was going to fall by committing the sin of stealing the cow.
As another side note I think all the partial incarnations are actually incarnations of Indra, who is a partial incarnation of Vishnu. The only reason they are listed as incarnations of Rudra or Vishnu is the authors know humans are not going to pay attention unless the supreme deity (or a supreme goal) is involved.
