Also, if we do chuck out unitarity, does that mean we can "break" experiments like stern Gerlach by just making them take a really long time?
It’s incredibly easy to lose coherence in other quantum experiments as well.
I probably should have specified: can you break stern Gerlach specifically by introducing isometry and the constructing an experiment that allows the particle to move through an expanding spacetime?
Ed: don't get hung up on "expansion of space is fuelled by light" or whatever, they only picked a photon for their thought experiment because it was easy to reason about.
Photons travelling cosmological distances (i.e., leaving galaxy clusters) in an expanding universe (like ours) will experience cosmological redshift.
When we look at distant clusters of galaxies with spiral shapes similar to those in our own (e.g. the Andromeda galaxy) we see the same spiral morphologies, but with reduced angle on the sky, reduced brightness, and a redshifting of the spectral lines associated with ionized gas, neutral hydrogen, and so on. The angle-brightness relationship is evidence of distance (if you are hundreds of metres from a lightbulb it won't seem as bright or as large as if you were right beside it), and the spectral lines are evidence of gas and dust (absorbing and re-radiating light), and the chemical composition of stars on the other side from us of that intervening absorptive material. If we have a smaller, dimmer, redder spiral behind a bigger, brighter, bluer (but still distant) spiral, we expect to see two distinct sets of red-shifted spectral lines. In fact, we see significant stacks <https://www.astro.ucla.edu/~wright/Lyman-alpha-forest.html>. The farther light travels, the redder it gets. More detail: <https://astronomy.swin.edu.au/cosmos/C/Cosmological+Redshift>
There are lots of ways to think about the cosmological redshift, but it is a readily observable feature of our universe, and can be compared with other readily observable features (the small position-dependent gravitational redshift which we can measure here on Earth; and the kinematic "special relativity" redshift reciprocally found between observers in uniform motion, likewise). Some details about local redshift: <http://www.leapsecond.com/pages/atomic-tom/> <https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experim...>. Cosmological redshift as an additional feature is so clear that it is more common in extragalactic astrophysics and physical cosmology to talk about the "z" (redshift) of distant galaxies than describing distance in terms of billions of light-years or megaparsecs.
"z" is a relationship between emitted light and detected light. If it's emitted in the past at say 500 nanometres (greenish), and is detected today at 1000 nanometres (in the near infrared), z = 1, and the emission happened between 7 and 8 billion years ago. (Further info: <https://apod.nasa.gov/apod/ap130408.html>; the table there captures the values for the acceleration of the expansion of the universe as known at the time it was prepared).
Under time reversal we expect that the 1000 nm photon "starts" here and ends up at the distant galaxy as a 500 nm photon -- a cosmological blueshift.
If we take a 500 nm photon from today and aim it into deep deep space it might fly off practically forever, becoming extremely infrared in the process. If we start with a very infrared -- radio -- extremely low frequency photon time-travelling backwards from the distant future, we get a green 500 nm photon here.
But what happens if we start billions of years in the future with a 500 nm photon using z=1? The wavelength halves, so "here" in the past we find a 250 nm photon, in the middle-ultraviolet (UV-C, good for killing germs!). If we start backwards-time-travelling green photon even further in the future, we end up with a photon even deeper into the ultraviolet. (Or, conversely, in our usual direction of time, if we launch a 125 nm photon from here, then in something like 40 billion years it would be detected as a green 500 nm photon, thanks to the cosmological redshift).
There is a symmetry: light going into the far future gets redder, light going into the far past gets bluer. But the symmetry isn't perfect because there is probably a minimum wavelength for light and probably no maximum wavelength. That's one challenge for unitarity. It's also not perfect in a universe with structure in it. The structure dilutes away in the future, so the reddening light is less and less likely to collide with things like galaxies or planets. The structure concentrates in the past, so the blue-ing light is more likely to colide with dense gas and dust. And the effects upon collision differ: a very long wave photon is unlikely to disturb whatever it runs into, but a very short wave ultraviolet photon can disrupt molecular bonds, strip electrons from atoms, or disintegrate atomic nuclei. In extremis it might become so energetic and so short-wavelength that it develops an event horizon, at least if it gets near any other matter.
We can do that extremis by starting our green photon many many trillions of years in the future. If we let it time-travel in the ordinary way, into the future, it just eventually becomes deep infrared. But if we let it time-travel back towards here-and-now, it would arrive from the future as an extreme gamma ray. Don't let that hit you, it'd blow you right up.
There are other broken time-travel symmetries that don't require cosmological distances or quantum behaviour, so we should no more expect to see this sort of super-energetic gamma ray around us than we see broken mugs of tea un-breaking themselves and leaping up onto a table in front of the paw of a bored cat. Quantum mechanics might strive to fully describe systems like cats introducing small, fragile, liquid-filled containers to the concept of gravitational free-fall, but (despite the many successes of the Standard Model of Particle Physics) can't. Maybe that's why Erwin Schrödinger thought so hard about doing something unfathomably mean to a domestic feline.
Finally, cosmological redshift is caused by the spacetime curvature of an expanding universe. The parts of the universe within galaxy clusters are not expanding (technically, the interiors and near-exteriors of galaxy clusters are poorly described by any expanding-spacetime metric, and well-described by families of collapsing-spacetime metrics), and the rest (all the space between clusters) is expanding gently enough that one has to travel across a lot of it to see a very strong (rather than merely technically measurable) effect. Since travel speed is capped at the speed of light, it would take a long time to get far enough from the Milky Way to notice the effects of traversing the expanding spacetime well outside it. Inter-galaxy-cluster distances are large though, and we can see very distant galaxies, so redshift accumulates. We see galaxies with redshifts of more than eleven (z = 11 means a 500 nm green photon from then gives us a 6000 nm mid-infrared one now).
There is stronger curvature to be found closer to home, so if you want to break a quantum experiment which only works in very flat spacetime, take the apparatus only a few hundred light years to a nearby neutron star in our own galaxy.
Indeed, whether there is unitarity at all in the presence of strong gravity has been a matter of debate for some decades, so you might end up taking a bunch of experimental physicists with you to try out other things around that compact object. (A black hole, with a horizon, is another good choice, since there are arguments about whether horizons physically special surfaces that somehow preserve or somehow obviously violate unitarity in ways that even the heaviest neutron star cannot -- best to visit a small black hole, with strong curvature at the horizon, and a huge black hole, with curvature at the horizon gentler than curvature here on Earth's surface. Of course there are arguments that outside the horizon you can't observe violations of or preservation of unitarity within, so you might have to wait around the black hole a long time for it to finally, totally, evaporate; in that case there's time to do a lonnng near-the-speed-of-light extragalactic trip too).
tl;dr for your last question: good question, and generalizes to related questions, but with nothing close to a settled answer available at this time.