"Stripping a virtuous man of virtue would be no good result."
Perhaps we should focus exclusively on the Buddhist doctrine of karmic rebirth here. Within the Buddhist framework, karma is just a law of cause and effect. There's no God and no designed scheme behind karma, so it has no end goal. Karma is simply a natural law. And Buddhist ethics is consequentialist. Good behavior is good because it has good results and bad behavior is bad because it has bad results.
As a statement of the Buddhist notion of karmic rebirth, I would point to the following passage from the Itivuttaka, where the Buddha says, "If this person [with a corrupt mind] were to die at this time, he would definitely be born in hell, as if a heavy load were to be dropped down on one's head. What is the reason for that, it is because his mind is corrupt. It is because of the mind's corruption that some beings in this world, at the breakup of the body after death, are reborn in the plane of misery..." and "If this person [with a pleased mind] were to die at this time, he would definitely be born in heaven...What is the reason for this? It is because his mind is pleased. It is because of the mind's confidence that some beings in this world, at the breakup of the body after death, are reborn in a good destination."(Itivuttaka 20-21)
It's interesting here that, according to the Buddha, the state of consciousness at the exact moment of death supersedes everything else that one has done. Why is this? I suppose because the state of mind that one is in at that final moment is the causal effect of all karmic events preceding it within one's lifetime. I propose, then, that all of the karmic actions throughout ones life only matter to the extent that they determine one's state of mind. If I meditate daily and do charity work on a regular basis, I am more likely to be in a calm and peaceful state at the moment of death. If I am habitually rude and hateful to those around me, I'm more likely to be in an unpleasant state of mind at the moment of my departure.
Now I'm asking, within the framework of generic subjective continuity or existential passage, why would we assume that the passage is from one conscious entity to the very next conscious entity that is born and not that the passage goes from that conscious entity to the very next entity with a similar baseline consciousness?
What prompted me to think about this is a passage in a work by Thich Nhat Hanh, where he is talking about people asking for his phone number or email so that they can keep in touch with him. He brushes off the suggestion and asserts instead that 'if you really want to be close to me, do the walking meditation as I do and, whereever you are, at that moment our states of consciousness will align and we will be the closest we could ever be, regardless of the distance between our bodies.' (I'm paraphrasing from memory) The reason he suggests this is because two points of consciousness that are aligned (or in the same state) are essentially identical. So if I meditate the way he does, in that moment, if not for the accidental features of our bodies and memories, our generic subjectivities or consciousnesses would be essentially the same.
Now, I want to suggest that we can take the idea of generic subjective continuity and formulate it where the link between lives is very much like that. If I cultivate virtue throughout my life, behaving in a good manner and cultivating good habits of thought, that will help me to cultivate a baseline consciousness that is relatively pleasant. Then, if I die, my consciousness will transfer to the next being born that is "on the same frequency" as I was. And so, we see here a model of generic subjective continuity that closely resembles the Buddhist concept of karmic rebirth.
Now, what happens if we meditate constantly and can achieve a state of mu-shin (empty-mindedness) and what if that is our state of mind at death? Well, then, I suggest that this would correspond to what the Buddha called pari-nirvana.
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As for your suggestions about cumulative virtue and moral progress, I don't think that we should expect the historical record necessarily to show this. Why? Because we only see the Earth and, presumably, there are an infinite number of worlds and an infinite number of conscious entities out there, so it could be that the cumulative effect is that virtue is increasing in the universe (or multiverse) as a whole. I'm not convinced that this karmic doctrine necessarily implies constant progress in virtue but, even if it did, expecting the historical record to hold evidence of that would be a fallacy of geo-centrism.
