There appears to be an assumption that this rage will indefinitely increase, thereby causing the size to become smaller than that which applies to forces, is my understanding correct?

This is a better response than I could've given. But let's talk about the Big Rip, because it's way more interesting than the Big Freeze. And for fart jokes.

As soon as something vanishes optically from our visible horizon in space-time, we will be free of its gravitational influence. We do know that there is more universe beyond via dark flow observations. So yeah, we'll start to see things "going dark", but we don't even know the exact size of the observable universe. It's believed to be 46-47 billion light-years away, and a billion light-years of margin is a lot. And yes, the universe is only 13.8 billion years old, some people have trouble reconciling an apparent discrepancy there.

What I'm really hazy on is whether or not the sizes of "fundamental" particles scales with universal expansion. Regardless, yeah, unless the physical constants change with time in lock-step with expansion (and they might, we don't know yet), there will eventually be effects on atomic and molecular structures, and then it all goes to hell pretty quickly after that, I imagine. I'm not well-versed enough in quantum mechanics to venture a guess as to how the strong, weak, and Coulomb forces will react, and in what order.

At the end of the big rip is the destruction of atoms. Is that a spontaneous conversion of atoms to dark energy, or something else?

Protons, neutrons and electrons are first separated from each other far enough to not interact. They might eventually have their mass converted to energy, as the diameters of quarks and electrons become the length at which information can no longer be communicated? This is actually a weird rabbit hole of not-so-well-established ideas, so I'm purely speculating.

Tom Cruise and I are already working on MI:6 (which is Mi6 British-themed, of course) about using the LHC to create a local safe-zone surrounding our solar system when all baryonic matter goes radioactive simultaneously as a result of universal expansion. Yeah, the Big Rip is ripe for Hollywood exploit.