I have posted elsewhere that there is no Lakshmi in the Ramayana version. If I am not mistaken there is a version in which kalakuta doesn't come out.
This is a long answer, so I made a table at the end, which you can skip to if you like.
In commentary for the Vishnu Purana, one translator gives us the following note:
There is some variety in the order and number of articles produced from the ocean. As I have observed elsewhere (Hindu Theatre, I. 59. Lond. ed.), the popular enumeration is fourteen; but the Rámáyana specifies but nine; the Mahábhárata, nine; the Bhágavata, ten; the Padma, nine; the Váyu, twelve; the Matsya, perhaps, gives the whole number. Those in which most agree, are, 1. the Háláhala or Kálakúta poison, swallowed by Śiva: 2. Váruní or Surá, the goddess of wine, who being taken by the gods, and rejected by the Daityas, the former were termed Suras, and the latter Asuras: 3. the horse Uchchaiśśravas, taken by Indra: 4. Kaustubha, the jewel worn by Vishńu: 5. the moon: 6. Dhanwantari, with the Amrita in his Kamańd́alu, or vase; and these two articles are in the Váyu considered as distinct products: 7. the goddess Padmá or Śrí: 8. the Apsarasas, or nymphs of heaven: 9. Surabhi, or the cow of plenty: 10. the Párijáta tree, or tree of heaven: 11. Airávata, the elephant taken by Indra. The Matsya adds, 12. the umbrella taken by Varuna: 13. the earrings taken by Indra, and given to Adití: and apparently another horse, the white horse of the sun: or the number may be completed by counting the Amrita separately from Dhanwantari. The number is made up in the popular lists by adding the bow and the conch of Vishńu; but there does not seem to be any good authority for this, and the addition is a sectarial one: so is that of the Tulaśí tree, a plant sacred to Krishńa, which is one of the twelve specified by the Váyu P. The Uttara Khanda of the Padma P. has a peculiar enumeration, or, Poison; Jyesht́há or Alakshmí, the goddess of misfortune, the elder born to fortune; the goddess of wine; Nidrá, or sloth; the Apsarasas; the elephant of Indra; Lakshmí; the moon; and the Tulaśí plant.
Yet this is not the full answer, for they are not agreed upon universally.
'Re-established thus in strength, the gods recommenced churning. After a while, the mild Moon of a thousand rays emerged from the Ocean. Thereafter sprung forth Lakshmi dressed in white, then Soma, then the White Steed, and then the celestial gem Kaustubha which graces the breast of Narayana. Then Lakshmi, Soma and the Steed, fleet as the mind, all came before the gods on high. Then arose the divine Dhanwantari himself with the white vessel of nectar in his hand. And seeing him, the Asuras set up a loud cry, saying, 'It be ours.'
"And at length rose the great elephant, Airavata, of huge body and with two pair of white tusks. And him took Indra the wielder of the thunderbolt.
But with the churning still going on, the poison Kalakuta appeared at last. Engulfing the Earth it suddenly blazed up like a fire attended with fumes. And by the scent of the fearful Kalakuta, the three worlds were stupefied. And then Siva, being solicited by Brahman, swallowed that poison for the safety of the creation. The divine Maheswara held it in his throat, and it is said that from that time he is called Nilakantha (blue-throated).
Vishnu Purana retelling:
From the ocean, thus churned by the gods and Dánavas, first uprose the cow Surabhi, the fountain of milk and curds, worshipped by the divinities, and beheld by them and their associates with minds disturbed, and eyes glistening with delight. Then, as the holy Siddhas in the sky wondered what this could be, appeared the goddess Váruní (the deity of wine), her eyes rolling with intoxication. Next, from the whirlpool of the deep, sprang the celestial Párijáta tree, the delight of the nymphs of heaven, perfuming the world with its blossoms. The troop of Ápsaras, the nymphs of heaven, were then produced, of surprising loveliness, endowed with beauty and with taste. The cool-rayed moon next rose, and was seized by Mahádeva: and then poison was engendered from the sea, of which the snake gods (Nágas) took possession. Dhanwantari, robed in white, and bearing in his hand the cup of Amrita, next came forth: beholding which, the sons of Diti and of Danu, as well as the Munis, were filled with satisfaction and delight. Then, seated on a full-blown lotus, and holding a water-lily in her hand, the goddess Śrí, radiant with beauty, rose from the waves.
"Then, after a thousand years from the heads of the serpent that is used as churning rope, namely the Thousand-headed serpent Vasuki, and when its fangs of Vasuki fanged the cliffs of Mt. Mandara, disgorged is a poisonous venom, which on melting the rocks of Mt. Mandara became the lethal and flaming haalahala
[...] Then after a thousand years a male personality and an epitome of Life Science, namely aayur veda... a highly righteous soul named Dhanvantari, with his arm-rest-stick and with his handy water-vessel, surfaced firstly, and also the Apsara-s with their remarkable elegance emerged later...
[...] then came up the heaven-sent Vaarunii, the presiding deity of hard liquors and also called as sura, the daughter of Varuna, the Rain-god, searching for her espousal... and oh, Rama, the sons of Diti have not espoused her, Vaaruni, the daughter of Rain-god, but oh brave one, the sons of Aditi have espoused that impeccable Vaaruni... Thereby the sons of Diti are asuraa-s and as such, the sons of Aditi are suraa-s and delighted and rejoiced are the gods on espousing Vaaruni.
[...] "Oh, Rama, the best among men, then emerged is the best horse called Ucchaishravaa... and then, a gem of a jewel, namely Kaustubha, and like that, amrita, the Supreme ambrosial elixir of gods...and oh, Rama, then there chanced a great ethnic havoc, caused by Ambrosia, for its possession, when the sons of Aditi have havocked the sons of Diti... and oh, brave Rama, all the asura-s and demons have arrived at a unity, and a ghastly war came to pass, which was perplexing to all the triad of universes viz., ethereal, real and surreal spheres...
Devi Bhagavata Purana retelling:
He then addressed Brahmā and said :-- “O Lotus-born! You also better go there and churn the Kṣiroda Ocean; when Lakṣmī will arise, give her to the Devas.” O Devarṣi! Thus saying, the Lord Kamalā went to His inner compartment. On the other hand the Devas, after a long time, reached the shores of the Kṣiroda Ocean. The Devas and the Daityas then made the Golden Mountain (the Sumeru) the churning rod, the Deva Kurma (the tortoise), the churning pot and Ananta Deva (the thousand headed serpent) the churning cord and began to churn the ocean. While churning was going on, by and by arose Dhanvantarī, Amrita (the nectar), the horse Uccaihśravā, various other invaluable jewels that were desired, the elephant Airāvata and the beautiful eyed Lakṣmī.
Padma Purana retelling:
Having thus ordered Jyeṣṭḥā, dear to Kali, all the gods, well-composed, again churned the Milky Ocean. O you of an auspicious face, then goddess Vāruṇī came up. Ananta, the lord of serpents, took her of beautiful eyes. Then Surā (spirituous liquor), adorned with all ornaments, came up. She graced with all (auspicious) marks became the wife of Garuḍa. Then bevies of celestial nymphs and divine and very strong gandharvas endowed with handsomeness and engaged in sweet singing, came up. Then Airāvata came up. Then the horse Uccaiḥśravas came up. Then came up Dhanvantari, Pārijāta and Surabhi giving all desired objects. Indra with a pleased mind accepted all these. Then in the morning when the sun rose on the Dvādaśī day, and when the Ocean was again churned by gods led by Indra, Śrī, Mahālakṣmī, the auspicious goddess of all the worlds, being praised by great sages with pleasing faces, came up.
[...] Then from the Milky Ocean the Moon came up.
Shiva Purana retelling:
- When the milk-ocean was churned the goddess of heaven sprang up from the ocean as the daughter of Bhṛgu who later became Viṣṇu’s beloved.
17-18. There also emerged—Dhanvantari, the moon, the Pārijāta tree, the horse Uccaiśśravas, the elephant Airāvata, wine, the bow of Viṣṇu, the conch, the cow Kāmadhenu, the jewel Kaustubha and the nectar.
- When it was churned again, the great poison Kālakūṭa blazing like the fire at the dissolution of the Yugas and terrifying the gods and the Asuras, came out.
|Element||Ramayana||Mahabharata||Vishnu Purana||Devi Bhagavatam||Padma Purana||Shiva Purana|
So from this, all that we get for certain is that Dhanavantri came from the ocean. But we have to filter through this information a little bit. The only versions here that fully retell the story are the Mahabharata, Vishnu Purana, and the Ramayana; the others are simply summaries or anecdotes intended to explain the birth of one character and happen to mention a few of the others. I'll leave you to parse through the table and interpret as you will, based on your definition of what the 'major retellings' are, but I think it's safe to say that Amrita, Halahala, and Lakshmi also all came from the Samudra Manthan.