I was waiting in this thread to see if somebody mentions an obvious problem in what you wrote. As you ask about some possible help in the form of different thoughts, I give you these:
in what you writes the problem is not really the Rebirth but the absence of an investigation in the metaphysical assumption you are keeping, which is non-rebirth.
You wrote the rebirth assumption should exist by faith or the authority of the mystical experiences. This is not very right. On the contrary, the rebirth assumption is supported by an enough logics which is absent in the non-rebirth case. Of course, there is also that plus of the mystical side and the memories of quite people. And this is a good support because we know there is no person in this world with some mystical experience or memories from a previous non-existence. This can sounds obvious but that obviety is philosophicaly auto-explanatory.
Despite we don’t have access to an empirical experience of this problem, there are enough logical resources to clean our attachment to non-rebirth and the logical incoherences of this metaphysical assumption and belief. This is the biggest part of this problem. We were not born in some cultural context with rebirth but in one with non-rebirth. Therefore, we cannot adopt the rebirth like a blind substitute for non-rebirth. First we should look in the strong errors in the metaphysical assumption of non-rebirth.
Few times we read about these obvious contradictions in metaphysics of non-rebirth. That’s logical because this is like a comfortable shared non-sense, working like a brain programming in us. It only works like a platform wtihtout foundations although useful to request proofs for other thing. We can see hordes of people requesting all type of proofs for rebirth while they didn’t request any for non-rebirth. Why so?. Because most people is dragging their own metaphysical assumption in a quite ignorant way, without asking about its real sense and logical authority.
In example: you uses “death” like a clear border between continuity and nihilism because the moment of death; between existence and non-existence. However, when we think about death, this is not only the immediate appearance of a physical body without activity. We are naming “death” to the belief in a metaphysical assumption of an stage in where there is non-existence. This is the inferred knowledge of “death” arising from the view of a body without any activity. However, here we forget that same stage (the same metaphysical assumption endowed with the same nature of non-existence) also existed before we were born. And it has not impeded our birth. One should think two times about this. This is a foundamental metaphysical contradiction dragged by all the people believing in non-rebirth.
I writes “dragged” because mostly they cannot see these obvious thing. Be in case of common people, academics even some buddhist teachers. This collective “forgetfulness” is sealed in that metaphysical packet because this is a a foundamental piece to keep that wrong view.
Many buddhist teachers don’t put emphasis in this issue because this problem is not a direct obstacle to enter in the stream, at least in a general way. However, the wrong view of non-rebirth will be a problem soon or later because it conditions a deeper understanding of Reality. This is a wrong view opposed to the continuity ruling the Nature and the whole Universe, and of course the continuity present in the Dhamma law.
Notice also with non-rebirth we are forced to do one very strange exception to that law: with oneself. Why so?. Nobody can answer to that. There is no logic available to keep that exception. At the end this only can sound amazing or funny, depending of the person.
There are still more things to say about the incoherences of non-rebirth. There are more although it would be long.
Many times we forget the healthy skepticism present in Buddha teaching should be directed first to check our own assumptions before those from other people. On the contrary, we will lack of clear thoughts to understand other ideas and assumptions.
The investigation of the own metaphysical assumptions we are carrying is a very needed task. Siddharta did it to become a Buddha and also we should do it.
Also I believe a main difficulty for this purporse is when these issues go deeper in existential terms, and it can require from a real honesty with oneself. There is too much people with auto-impossed limits as soon they perceive Dhamma can touch other “important” worldly implications. I mean the people who see the Dhamma from a utilitarian point of view, for third purposes be political, scientifical, ideological or whatever. In such cases probably happens what an old philosopher said: the Truth is a demanding lady who don’t threw herself into the arms of a nobody.
Some different thoughts. Hope it helps.