Even when the universe dies and a googolplex years pass between its death and some random event that creates a new universe, those years cannot be experienced. They will only exist in hindsight for whatever beings arise afterwards.
Starting from the materialist premise that consciousness (or subjective perception of qualia) arises from the coincidental configuration of a specific set of physical matter, if that matter is completely annihilated by antimatter in the process of the birth of a new universe, or perhaps if that matter is disassembled down to the level of subatomic particles (quarks, bosons, etc.) and made to behave fundamentally differently in the new universe, then wouldn't at least the annihilation-by-inverse-antimatter scenario put a true end to subjective experience for any matter which existed and behaved according to the rules of the universe that exist now?
Any specific instance of some cluster of matter (and antimatter) generated by Hawking radiation wouldn't be the same instance of matter which had that same continuity of subjective experience. Continuing the cycle of reincarnation in the sense Clark lays out seems like it would be impossible; a Buddhist which asserts that reincarnation continues from the end of one universe to the next after an arbitrarily and unfathomably long timespan would have to have an alternate explanation for how reincarnation works, one that might rely on some form of idealism (and that contradicts the Buddhist conception of there being No Souls independent from the material world). Even if some perfect replica of our universe eventually spontaneously emerged (such that the structure of spacetime is identical throughout) from a big bang, it would consist of entirely new matter generated ex nihilo by Hawking radiation, and the existence of some identical configuration would still imply a break in the continuity of subjective experience through the reincarnation of either a unique persistent set of matter or an continuous Ship-of-Theseus cluster of matter. The only possible causal (and thus karmic) link would be the behavior of the black holes left over from the previous universe which generate the next one, iterated arbitrarily many times.
I would like to thank you for addressing my responses in good faith so far. This conception of no escape from the inevitable pain brought about by subjective experience of being alive is still utterly terrifying to me, and I'm motivated to fully understand it from a grounded, scientific, materialist perspective.