Interesting. Is this also related to the no-self doctrine?

Yes, phenomena ultimately lack a substantial essence [svabhāva] and therefore lack an essential identity, this is the real meaning of selflessness or no-self [anātman].

The self is an illusion and a byproduct of ignorance manifested from our inability to comprehend our interconnected psychological elements lacking genuine essence and thus, creating an illusory entity?

Precisely, although I would say the self merely "appears" as a result of our inability to recognize its genuine nature as insubstantial and illusory. "Appear" being the operative term because if we understand that the perception of identity results from a failure to recognize a lack of essence in phenomena, then it is equally understood that the misconception of identity is a mere appearance and thus nothing is ever truly "created" at any point.
When we perceive identity in persons and phenomena we are only ever relating to our own ignorance, like seeing a rope in a dark room and mistaking it to be a snake. The snake merely "appears" as a result of our failure to recognize the rope, the snake never actually originates or is created at any point in time, and when we recognize the actual nature of the alleged snake, then we see it never originated in the first place.

Would that be something close to what dependent origination means in that context?

Yes this is exactly what dependent origination means. Phenomena only appear to originate in dependence upon our ignorance regarding their actual nature. Nāgārjuna is very clear about this, for example in his Yuktiṣāṣṭikakārikā he states:

When the perfect gnosis sees that things come from ignorance as condition, nothing will be objectified, either in terms of arising or destruction.

And,

Devoid of locus, there is nothing to objectify; rootless, they have no fixed abode; They arise totally from the cause of ignorance, utterly devoid of beginning, middle and end.

This has large scale implications as well, which is why Nāgārjuna sometimes uses the example of the world itself. From the same text:

Since the Buddhas have stated that the world is conditioned by ignorance, why is it not reasonable [to assert] that this world is [a result of] conceptualization? Since it comes to an end when ignorance ceases; why does it not become clear then that it was conjured by ignorance?

The unreality of the world is also mentioned in his Acintyastavaḥ and Lokātītastava, where it is said it manifests due to the imagination, likened to a mirage, or a child that is born, lives and dies in a dream.
This is why many adepts are explicitly clear that dependent origination [pratityasamutpada] is synonymous with a lack of origination [anutpāda], because phenomena that originate in dependence on ignorance as a cause, never actually originate at all. We see many adepts state that they are equivalent, Candrakīrti for example:

The perfectly enlightened buddhas-proclaimed, "What is dependently created [dependently arisen] is uncreated [non-arisen]."

Or Mañjuśrī:

Whatever is dependently originated does not truly arise.

Nāgārjuna, once again:

What originates dependently is unoriginated!

Moving on...

Of course i assume that nirvana is needed for that ignorance to subside.

Yes, nirvana is defined as the total cessation of ignorance, or the total cessation of cause for the arising of samsara.

I guess that makes rebirth somewhat plausible in the sense that the summation of our elements are transferred without an actual identity since our identities are illusion,

Right, essentially all that is reincarnating (or being 'reborn') are causes and conditions, which is the only thing that is ever occurring. Afflicted aggregates beget afflicted aggregates, each serving as simultaneous cause and effect. So there is no individual 'soul' or entity as such that is being reborn... and ironically, the fact that there is no inherent soul or permanent entity is precisely why rebirth is possible.
Causes and conditions proliferate ceaselessly where there is a fertile basis for said proliferation. These factors create the illusion of consistency in conditoned phenomena (phenomena capable of existing and/or not-existing), and the illusion of an enduring entity which was allegedly born, exists in time and will eventually cease. Ultimately, the so-called entity is simply patterns of afflicted propensities, habitual tendencies etc. however over time, these factors become fortified and solidified creating the appearance of an autonomous sentient being. The point of the buddhadharma is to cut through this dense build up of conditioning and ideally dispel it altogether.
Rebirth is the result of unceasing karmic (cause and effect) activity. If ignorance of the unreality of that activity is not uprooted, then said activity simply persists indefinitely. An easy example is the fact that we wake up in the morning with the feeling that we are the same individual who fell asleep the night before, however all that has persisted are aggregates that appropriate further aggregates, ad infinitum. We as deluded sentient beings do not realize that there is no actual continuity to the appearance of these so-called aggregates, and so that ignorance acts as fuel for further unfolding of the illusion of a substantiated, core, essential identity in persons and phenomena (and the habitual behavior and conditioning predicated upon that ignorance serves as the conditions for the continual arising of said illusion). If these causes and conditions are not resolved then the process simply goes on and on through apparent lifetimes, the entire process being akin to an unreal charade.
Nāgārjuna is also very clear about this, for example from his Pratītyadsamutpādakarika:

Empty (insubstantial and essenceless) dharmas (phenomena) are entirely produced from dharmas strictly empty; dharmas without a self and [not] of a self. Words, butter lamps, mirrors, seals, fire crystals, seeds, sourness and echoes. Although the aggregates are serially connected, the wise are to comprehend nothing has transferred. Someone, having conceived of annihilation, even in extremely subtle existents, he is not wise, and will never see the meaning of "arisen from conditions."

and In his Pratītyasamutpādakarikavhyakhyana, Nāgārjuna states in reply to a question:

Question: "Nevertheless, who is the lord of all, creating sentient beings, who is their creator?"
Nāgārjuna replies: "All living beings are causes and results."

And in the same text:

Therein, the aggregates are the aggregates of matter, sensation, ideation, formations and consciousness. Those, called "serially joined", not having ceased, produce another produced from that cause; although not even the subtle atom of an existent has transmigrated from this world to the next.

It is a completely agentless process driven by affliction.

which is in stark contrast to Pythagorean or Platonic ideas of transmigration of the soul.

Yes, it is also in contrast to the Hindu definitions of reincarnation that involves a substantial essence.

So children remembering their past lives isn't as implausible as previously thought.

Certainly not implausible, karmic imprints on the mindstream persist.