> baryons will fall apart on a [lonnnng] scale

I doubt it. A more practical problem might be keeping baryons from falling into black holes or escaping to infinity (in which case, nobody will care if they decay or otherwise disintegrate eventually).

There's evidence (from the solar system and from gravitationally bound multi-body systems outside it) that there is to all practical purposes no metric expansion of space within clusters of galaxies, which are the largest known gravitationally-bound system, nor any subsystem within such clusters. A hypothesis that involves the metric expansion (or a "fifth force" form thereof) disintegrating atomic nuclei is at this point very far-fetched.

Instead, let's consider a "swiss cheese" cosmology where in the large galaxy clusters are homogeneously and isotropically embedded within a "cheese" of expanding Robertson-Walker spacetime. Each cluster can be represented by an eventual vacuole -- a hole in the cheese -- initially filled with gas and dust. They are "eventual" vacuoles because gravitational collapse will tend to condense the gas and dust into the centre.

Mathematically, in the large these vacuoles can be represented as Lemaître-Tolman-Bondi-style collapsing dusts, where we can recurse, with subsystems like galaxies also behaving over long timescales as LTB collapsing dusts, likewise galactic nebulae and star systems. Everything inside a galaxy cluster tends to condense; and all galaxy clusters end up with more space between them over time.

In solving "swiss cheese" cosmologies, or recursive LTB-style systems, we can employ an Israel-Darmois thin-shell junction as a boundry between the subsystems on which we can stitch together fractions of geodesics of matter and light travelling across the junction. For example, simplifying by among other things employing maximal spherical symmetries, an isotropically radiating star sends photons across the nearest junction into its isotropically radiating nearly spherical galaxy; the galaxy shines into its cluster across a junction; the cluster shines into the "cheese". We can study the flow of radiation out of the topmost LTB vacuole into the "cheese". We can also study the flow of thin wispy stuff -- the CMB, but also radiation, neutrinos, and cosmic rays from distant galaxy clusters -- from the cheese into the vacuole.

For physically plausible arrangements of this sort of model, galaxy clusters barely change their mass-energy at late times (i.e., from ca. ten billion years ago to the practically infinite future), even though some gas (in the most general sense of baryons, photons, neutrinos, and so on) escapes them. Adding in colliding galaxy clusters (like Bullet) in small numbers doesn't really change this picture.

The baryons and other gas that remain within the "topmost" thin-shell pretty inevitably condenses into ever larger sets of black holes, which merge into ever larger black holes at the centres of each vacuole. Hierarchical supermassive black hole mergers might keep these giant black holes always colder than what's left of the ever thinning, ever colder cosmic background, or at least they will gobble up practically all the baryons in today's "topmost" holes-in-the-cheese, save for the small amount that drifts out into the expanding cheese (too slowly to ever fall into a second vacuole, but fast enough to escape their parent vacuole forever).

In the far far future -- ignoring the Boltzmann Brain problem -- baryons will probably only exist in the "cheese" at great distances from the ultramassive black holes that ate all the others. The Boltzmann Brain problem isn't so bad: very occasionally baryons will spontaneously appear very briefly before disappearing again. However, such fluctuations can generate implications for black hole evaporation.