three-lives interpretation (traditional Theravada)
This is not found in the suttas. In MN 38, for example, the child is born, grows, becomes attached to sensual pleasures & then experiences Dependent Origination. Then the same child, now a man, becomes a monk, attains jhanas and eradicates dependent origination (while his sense organs are consciousness of sense objects). MN 38 also says D.O. is experienced in the here-&-now, independent of the Buddha. MN 38 shows there is no such thing as three-lives.
birth-as-arising-of-self-view interpretation (Buddhadasa?)
"Jati" means "self" or "social identity" in India. It has never ever meant anything different to that. "Jati" in the suttas is literally defined as the "production of beings from the appearance of aggregates". "A being" ("satta") is literally defined in the suttas (SN 5.10 & SN 23.2) as a "view of clinging". Buddhadasa is close to literally in accordance with the suttas. "Jati" is the production of the self-view of "a being" or "beings", both internally & externally. Please abandon self-views and realise this reality. There are five aggregates, such as the five aggregates that breast fed you. From these five aggregates, the mind creates the view of two "beings" called "my mother" and "me". In reality, there is only five aggregates. Dhammapada says: "Kill mother; kill father". Buddhism 101.
and the impressions (sanskaras) plus naming-and-forming interpretation (Mahayana).
In SN 12.2, sankhara is not "impressions" and nama-rupa is not "naming-forming".
However, for a living arahat, what happens to the nidānas of mental formations (saṅkhāra), consciousness (viññāṇa), name-and-form
(nāmarūpa), sixfold sense base (saḷāyatana), contact (phassa), feeling
(vedanā), becoming (bhava) and birth (jāti)?
The sutta definition of Nibbana in MN 26 includes: "sabba saṅkhāra samatho", which means "calming of all sankhara". Therefore, in Nibbana, the three sankhara, namely, in & out breathing (kaya sankharo), vitakka & vicara (vaci sankharo) and perception & feeling (citta sankharo) are calmed. They are not destroyed. What is destroyed is craving & other defilements, namely, ignorance, attachment, becoming, birth & aging-&-death. Buddhism 101.
Suttas such as MN 38, Iti 44 and SN 22.53 say the arahant remains consciousness, with sense organs, sense contact & feelings. Since the arahant remains consciousness, obviously nama-rupa (mind-body) remain, per SN 12.67, SN 22.82, etc, which says consciousness is caused by nama-rupa.
As for "becoming" and "jati", these are defilements and they end per MN 38, which says "becoming" & "jati" cease when the "eye sees the form". "Becoming" is an "asava". Many suttas say the asava of becoming ends. "Jati" also ends. All arahants declare the ending of "jati". Except the Buddha. The Buddha declared: "This is my final birth" because the Buddha has the social identity of "The Buddha". Where as the arahant disciples have no special "jati" therefore they end "jati". MN 140 says because the arahant does not conceive "I am", the arahant is not "born"; does not age; does not die.
Buddhadasa taught Dependent Origination correctly, even though not completely. However, Dhammadhatu, exclusively on Buddhism Stack Exchange, explains D.O. fully and completely. Have faith & believe. When you realise Dependent Origination is not about reincarnation, you might realise Buddhism has nothing for you & decide to leave Buddhism and join Christianity or Hinduism; thus do good kamma by giving up creating obstacles for others by misrepresenting the Dhamma. In Buddhism, you are allowed to leave Buddhism. There is no crime of apostasy in Buddhism.