Let us clear up some things.
The end of an expanding universe is a matter of models.
The concept of mass is connected with energy as
for each individual particle. E and p are a four vector ruled by Lorenz transformations.
For a single particle that is the momentum energy four vector of the particle, and when it is at rest m is the rest mass of the particle. For more than one particle it is called the invariant mass, and when they are all at rest, it is the addition of their rest masses. When in motion, which is the usual state of particles in vacuum, there will always exist an invariant mass for an agglomerate of particles, and certainly for the universe.
Even zero mass particles can have (in a group) an invariant mass when more than one , as the existence of the pi0 meson demonstrates.
if two unlike-charged particles come close to each other, they will move towards each other and disappear to become light energy.
This will happen, an annihilation, only if all the quantum numbers are equal and opposite, and depending on the model the debris may be massive. Proton antiproton annihilate into a lot of mesons which in the end decay into leptons and photons, i.e. electrons positrons and neutrinos. It is at the end of the chain of decays that one may talk of end particles.
In the standard model of particle physics protons do not decay. In the standard model of cosmology there is observed baryon asymmetry , thus one expects protons to retain their identity to the end of time. BUT it is sure that there will be an extension of the standard model necessary due to small discrepancies , and in these extensions protons will decay and neutrinos have (small) masses and in this case everything will be photons at the very end of the decay and interaction chains, light of very large wavelength ( low energy photons due to the expansion of the universe).
This wasn't covered in the book, but unless I've misunderstood things (which is quite likely), there will be a point when all of the mass in the universe has been reduced to zero after all the particles have paired up and become photons?
You have misunderstood, all the rest masses of individual photons will be zero, but they will carry energy and momentum ( however small) and move with velocity c always, thus there will be an invariant mass from the addition of all the four vectors of the universe's photons, the end particles if protons decay.