> inhabitants of a block universe could experience time as sequential without a real sequential ordering of universe states

tl;dr: I don't think Boltzmann brains count as "inhabitants" because their worldlines are so short. Considering together a select set of available Boltzmann brains does not really admit something that looks like a long but complicated worldline. By virtue of being a fluctuation in a thermal bath in equilibrium a BB does not affect the wider universe; a Boltzmann flashlight can't blink out a message in Morse code.

The herd of elephants in the room is the exp(- \Delta S) suppression of fluctuations of size \Delta S out of equlibrium.

I think you are saying that we can imagine a set of some billion billion ephemeral Boltzmann brains each having memories associated with a unique fraction of a false life. I agree we can imagine that, but at the cost of having exact duplicates and many many more ephemeral Boltzmann brains with corrupted and even wholly unrelated false memories.

The true causality is the history of the thermal bath and not the memories of the brains.

In principle we can distinguish between a chosen set of same-false-life-at-different-stages Boltzmann brains and a real human with a very complicated FTL-and-time-travel worldline because at each point on the worldline the latter gets stress-energy ("signals", if you like) from the predecessor point, and also from (and to) each point's neighbours not on the same worldline. That is, our real traveller can detect the thermal bath temperature (which matters in an expanding cosmology) and leaks out metabolism photons to infinity. Ephemeral Boltzmann brains do neither.

The "virtual life" Boltzmann brains -- as you note -- do not have to be ordered in any way. I would go further: brains with immediately neighbouring fractions of the virtual life's false memories can be totally causally disconnected, not just causally disordered.

So I don't think the thought experiment says anything other than the Poincaré recurrence theorem admits states that are close (but not arbitrarily close or exact) to the initial state. That is, BB_final will recur, but so will BB_final-minus-one-nanoseconds-of-false-memory, BB_final-minus-two-nanoseconds-of-false-memory, ... but in some arbitrary point in the system's evolution. I don't think that's surprising.

There will also be brief ephemeral fluctuations into (and out of) mouse brains, cockroach brains, microchips, Jeep Wranglers, brains with memories of having lived lives as little green men from Mars, and so on and so forth. If you have BBs full of false human memories, without some unknown suppression mechanism you will also have BBs full of false nonhuman memories, and nonhuman BBs, especially smaller and less complicated ones (\Delta S being much smaller in those cases).

I also don't think it says anything about our universe, since we simply do not know enough about dark energy to make confident guesses about the very far future (i.e., does it really asymptote to de Sitter with the thermal bath from a dS horizon?). We also don't know if protons are stable that far into the future. However, with what we do know (which is not enough), the far future looks pretty empty. If there aren't RQFT interactions at GUT-scale energies that allow for violations of baryon and lepton numbers, maximum entropy in the far future (>> 10^33 years) still fairly low, but also the path to new nuclei from the (photon-dominated) thermal bath probably means no BBs at all (effectively all baryons are behind horizons by ~10^{10^10} years from now, and significant numbers BBs in our future light cone are expected not much earlier than ~10^{10^50}, although of course if BBs can happen at all, the very occasional individual BB may have its ephemeral moment at any time including today.)

So if there are BBs with false memories of human lives, they are so far in the future that an entire 2020s-style solar system fluctuating into existence and persisting (or a time-traveller who reaches that future) could not recover anything like our present cosmology. At best, via a strong Lorentz boost, they might detect relic and horizon photons, and maybe splatter their windscreens with the occasional BB.

The fluctuated-and-persisting-solar-system scientists would quickly realize its false memories of skies full of stars and galaxies were not true memories. A real time-traveller would probably just try to measure what's left of the CMB or find another marker of the cosmological scale factor.

(The time travel can have been to-the-future-only by something as boring as spending a lot of time moving close to the speed of light.)

Not discussed yet: what to do about fluctuations in fields which obey conservation laws that result in antiparticles. My fast answer would be: that's one reason BBs are so short lived; they are ripped apart by matter/antimatter annihilations.