Yes, with this I wholly agree, so my post here also would be probably the last. All I can say, it was a pleasure to disagree with you 
I will summarise what akalika approach to DO is, not in hope to arrive at agreement with you, but perhaps make it for you easier to know with what you disagree😁
…let the past be, Kaccāna, and let the future be. Let a wise man come, one who is honest and sincere, a man of rectitude. I instruct him, I teach him the Dhamma in such a way that by practising as instructed he will soon know and see for himself: ‘Thus, indeed, there rightly comes to be liberation from the bond, that is, from the bond of ignorance.’ MN 80
Rebirth depends on ignorance. Liberation from ignorance solves the problem of rebirth.
Dependent arising offers direct knowledge when there is this (ignorance) this is (conceit “I am”).
Puthujjana doesn’t see dependent arising so he uncritically accepts the attitude “I am” and provoked by it, creates self-image of “what I am”. He is not only certain that he is, but has a more or let precise image of himself.
Seeing of the Four Noble Truths leaves the attitude “I am” intact but prevents sekha from creating self-image. In other words one who sees dependent arising is free from attavada. The main difference between him and puthujjana is not the conceit “I am” but the understanding of it.
Puthujjana is certain that “I am”, sotapanna is certain that the attitude “I am” is dependently arisen on the ignorance here and now.
In other words sotapanna sees timeless direct relationship between ignorance and the attitude “I am”.
Now, you seem to say that as long as there is the attitude ‘I am’ there is organization of the five faculties of eye, ear, nose, tongue, and body. (SN 22 :47) Which of course means rebirth. But this is a direct knowledge of the Buddha, puthujjana who succeeded to see dependent arising merely replaced his certainty of being with direct knowledge that nibbana is the cessation of being now and here.
So our disagreement on the surface seems to be not very important since whether sotapanna knows directly rebirth or not, he can be the victim of it only for seven following existences. Unfortunately any interpretation which doesn’t insist on sine qua non relationship between the items of dependent arising prevents one to see it. (According to Ven Nanamoli Thera and I humbly agree with him).
You call it non-rebith interpretation. But aim of seeing dependent arising is to remove the rebirth by offering the understanding that one’s own birth is impermanent, sankhata or determined and dependently arisen on present ignorance. And only one who thinks about himself as born, can be reborn. Based on this understanding, sotapanna practices Dhamma. But how can puthujjana practice Dhamma properly if he doesn’t see that conceit “I am” is dukkha and it depends on present ignorance?
So as a matter of fact your rebirth-interpretation deserves its name since it leads to rebirth by not taking into account that dependent arising is the structure of being, has nothing common with time, and that it merely restates formula:
All sankharas are impermanent.
All sankharas are dukkha.
All things are not self.
It is so because the first item of dependent arising is always sankhara for the following item which is sankhata dhamma, and as such not-self. The aim of dependent arising is to help one abandon attavada, not to explain rebirth. Absence of attavada guarantee freedom from rebirth. It is enough to read Dr Stevenson’s work to know that there is rebirth, unfortunately however good is his research, it doesn’t help one to abandon attavada.
I don’t know with how many things in this post you disagree, but let that be. However I hope I stated things in this way so you clearly see with what you disagree, which unfortunately wasn’t the case with Bhikkhu Bodhi, who first had created his own interpretation of Nanamoli and Nanavira ideas, and than disagreed with it.*
And in shortest the main idea of dependent arising can be stated as:
To be is to be contingent: nothing, of which it can be said that ‘it is,’ can be said to be alone and independent. But being is a member of the paṭicca-samuppāda as arising which contains ignorance. Being is only invertible by ignorance.
The destruction of ignorance destroys the illusion of being. When ignorance is no more, then consciousness no longer can attribute being (pahoti) at all. But that is not all; for when consciousness is predicated of one who has no more ignorance then it is no more indicatable (as it was indicated in MN 22). Nanamoli Thera
Nanamoli Thera on Explanation and Rebirth
What is one trying to do in explaining rebirth? This consciously organized life is like a home garden in an endless jungle the edge of which is like death. To explain death and rebirth is like trying to explain the jungle in terms of the house and garden. Or again, the house is built of bricks and tiles made of clay, and beams made of jungle trees. Explaining rebirth is like trying to explain clay and trees in terms of the familiar made-up bricks and fashioned beams.
*Bhikkhu Bodhi:
An unbiased and complete survey of the Nikáyas, however, would reveal that the problem of dukkha to which the Buddha’ s Teaching is addressed is not primarily existential anxiety, nor even the distorted sense of self of which such anxiety may be symptomatic. The primary problem of dukkha with which the Buddha is concerned, in its most comprehensive and fundamental dimensions, is the problem of our bondage to samsara—the round of repeated birth, aging, and death.
If phrase “distorted sense of self” means something, surely it must mean attavada. But abandoning attavada is precisely what makes puthujjana ariya and is the most important task to perform if one wants to liberate oneself from samsara.
Or Ven Analayo, who’s “learned” article on Nanavira Thera contains such nonsense:
the mistaken notion of a self, held by some contemporaries of the Buddha.
So according to Ven Analayo some contemporaries of the Buddha were victims of attavadupādāna. What about others?
With metta, and see you at the next our disagreement on other subjects