In response to your post above:
My understanding is dukkha as the 2nd characteristic is not the same as the dukkha of paticcasamuppada. Dukkha as the 2nd characteristic is the ‘unsatisfactoriness’ of impermanent phenomena, as described in the Maggavagga of the Dhammapada, whereas the dukkha of paticcasamuppada is mental torment, or psychic irritants, as explained to to Nakulapita in SN 22.1Rebirth is very much part of the teaching of dukkha, which means it is also part of the teaching of anicca and anatta, making it very much part of the teaching of paticcasamuppada.
An ocean of tears
"Which is greater, the tears you have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — or the water in the four great oceans?... This is the greater: the tears you have shed...
"Long have you (repeatedly) experienced the death of a mother. The tears you have shed over the death of a mother while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — are greater than the water in the four great oceans.
"Long have you (repeatedly) experienced the death of a father... the death of a brother... the death of a sister... the death of a son... the death of a daughter... loss with regard to relatives... loss with regard to wealth... loss with regard to disease. The tears you have shed over loss with regard to disease while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — are greater than the water in the four great oceans.
"Why is that? From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released."
— SN 15.3
My understanding is the Buddha did not use the word “transmigration”. Bhikkhu Bodhi uses the word ‘roaming’. My understanding of this sutta is the ‘four great oceans’ is a simile. One person being able to cry more tears than the four great ocean is an impossibility because the water cycle recirculates. To accept this sutta literally would mean 6 billion human beings have cried more tears than the four great oceans.
My thoughts are that this sutta is referring to how a person mentally repeatedly experiences the death of a loved one. My understanding is that it is not related to comprehending the Four Noble Truths because comprehending the Four Noble Truths results in the cessation of suffering rather than crying & weeping.
This sutta shows how the mundane right view leads to asava and acquisitions. Because of the right view that mother & father loved us and mother & father are “beings”, crying & weeping is the result of this “good karma”.
This precious human birth
"Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind from the east would push it west, a wind from the west would push it east. A wind from the north would push it south, a wind from the south would push it north. And suppose a blind sea-turtle were there. It would come to the surface once every one hundred years. Now what do you think: would that blind sea-turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole?"
"It would be a sheer coincidence, lord, that the blind sea-turtle, coming to the surface once every one hundred years, would stick his neck into the yoke with a single hole."
"It's likewise a sheer coincidence that one obtains the human state. It's likewise a sheer coincidence that a Tathagata, worthy & rightly self-awakened, arises in the world. It's likewise a sheer coincidence that a doctrine & discipline expounded by a Tathagata appears in the world. Now, this human state has been obtained. A Tathagata, worthy & rightly self-awakened, has arisen in the world. A doctrine & discipline expounded by a Tathagata appears in the world.
"Therefore your duty is the contemplation: 'This is stress...This is the origination of stress...This is the cessation of stress...This is the path of practice leading to the cessation of stress.'" — SN 56.48
Why do we wander in samsara?
"It's because of not understanding and not penetrating four things that we have wandered & transmigrated on such a long, long time, you & I. Which four?
"It's because of not understanding and not penetrating noble virtue that we have wandered & transmigrated on such a long, long time, you & I.
"It's because of not understanding and not penetrating noble concentration that we have wandered & transmigrated on such a long, long time, you & I.
"It's because of not understanding and not penetrating noble discernment that we have wandered & transmigrated on such a long, long time, you & I.
"It's because of not understanding and not penetrating noble release that we have wandered & transmigrated on such a long, long time, you & I.
"But when noble virtue is understood & penetrated, when noble concentration... noble discernment... noble release is understood & penetrated, then craving for becoming is destroyed, the guide to becoming (craving & attachment) is ended, there is now no further becoming."
AN 4.1
I disagree with your opinion that inferences of rebirth in these suttas are tied directly to the Four Noble Truths. My opinion is the very opposite.
Human minds wander in samsara because they have not understood & not penetrated the Four Noble Truths. These suttas show what I posted earlier about two kinds of right view. Minds with the mundane right view wander in samsara, whereas minds with transcendent right view of the Four Noble Truths are liberated from spinning around in samsara.
So to conclude, to me, the explanation you have provided isn't convincing, as these suttas are about minds that have not realised the Four Noble Truths.
with kind wishes,
Aloka