This reminds me of some very old debates in Indian philosophy.

I'm assuming your argument here is based on Thomas Clark's theory of "generic subjective continuity" proposed in Death, Nothingness, and Subjectivity. If so, I think it would have been good to reference that work. If not, you should check that out.

I have a little bit of a problem following the progress over lifetimes argument and the argument there seems to be related to Nietzsche's idea of "eternal return." I don't think there's any reason to assume a recurrence just because eternity/infinity is assumed. To use a mathematical example, imagine a line extending infinitely in both directions. You can plot an infinite number of points on it. There's an infinite number but none of the numbers or points recur. There is never a repetition or recurrence. In fact, the probability of recurrence, even granting infinity here, is still non-existent. And I think eternity (infinity in time) may well look more like this number line example so that recurrence is not a thing. It could very well be the case that each new Big Bang gives rise to a universe in which the laws of nature are radically different from those of this universe, such that the same sorts of particles and elements and phenomena don't remain a constant feature of any two universes. Also, time could very well be a local phenomenon that doesn't apply outside of our universe, such that all things are occurring simultaneously/instantly-eternally from an ultimate perspective, so it may not make sense to even talk about probability and infinity in time.

I think it would be better here to interpret this less along Vedic lines as implying reincarnation and instead to interpret it as implying something like the Buddhist concept of rebirth. That's what it looks like to me (not like reincarnation, but like rebirth). In the reincarnation theory, there is an atman (soul/self) that is reincarnated (transmigration of soul into another body). In Buddhism, there is the doctrine of anatman (not-self), that there is no soul or self to be reincarnated. The "self" is illusory. Consciousness continues after death, but "you" do not. And this is very much a "generic subjective continuity" rather than a universal consciousness—Buddhism negates the Hindu or Vedic concept of atman/Brahman (individual self/universal self) with it's assertion of anatman/sunyata (not-self/emptiness).

The idea of there possibly being "only one conscious entity who, piece by piece, experiences everything...A god not of creation, but of experience" seems to me to align with the Vedic concept of Brahman and the modern "Buddhist" concept of Tathagatagarbha (both concepts that I think Gautama Siddhartha, the Buddha, was actually flatly rejecting when he proposed the anatman/not-self doctrine). The Tathagatagarbha doctrine in modern Buddhism seems to be a reversion back to the Advaita Vedanta (Hindu) interpretation of things. Tathagatagarbha as atma-paramita is just the Hindu Paramatman revived, the negation of Gautama's anatman/sunyata philosophy.