There are multiple reasonings, and there is no consensus on this site which one would be the right one.
I will give you the one I think is the most logical.
When a photon interacts with an atom in the glass, three things can happen:
elastic scattering, the photon keeps its energy and phase and changes angle
inelastic scattering, the photon gives part of its energy to the atom, changes phase and angle
absorption, the photon gives all its energy to the atom, and the absorbing electron moves to a higher energy level as per QM
Now in the case of glass, it is elastic scattering. This is the only way a mirror image can be built, and the photons keep their energy and phase.
This is Rayleigh scattering, and specular reflection. In this case the wavelength of the photons is much bigger then the atoms of the glass.
Imagine that not only mirrors, but glass can give a mirror image too. What is the difference between the image you see as a mirror image in the glass, and the image that is transmitted through the glass? The only difference is the angle. One is called reflection (mirror image), and the other is called refraction (image travels through the glass). In the case of reflection, photons travel back in air, and in the case of refraction, photons travel forward in the glass.
Both cases the mirror image is kept, and the only way to do that is elastic scattering.
Now to answer your questions:
When someone questions how light can re-accelerate after slowing down in a glass medium, the common answer is that it never really slows down, it is absorbed by the atoms and then released.
It is not absorption, re-emission. In that case the photons would be reflected decoherently, and they would change energy and phase. With absorption, the re-emission can happen in different directions too, and the electron can come down in multiple steps, releasing multiple photons, when it was only absorbing one. So this way a mirror image cannot be built.
It is elastic scattering.
Have there been any confirmations that this is the reason why light appears to slow down, or is this speculation, the best guess we have?
No, there is no proof for that, on the contrary. It is elastic scattering, and the reason why EM waves slow down, is that the wavefront slows down.
Photons are traveling in vacuum always with speed c, when measured locally. Now a photon always travels in vacuum, inbetween the atoms. So it always travels with speed c.
What slows down is the wavefront. Why? The reason is that with elastic scattering, the photons need time for the electromagnetic interactions. Those interactions take time, and so the wavefront changes phase and slows down.
Now the way you measure the speed of EM waves in glass is you take the distance, and divide it by the time the wavefront will need to reach the end of the medium. Since the wavefront slows down, EM waves travel slower in media then c. Photons still travel with speed c in the glass between the atoms.
I'm thinking the apparent speed reduction could be estimated by knowing the density of the glass and calculating in the absorption/emission time?
You are right with the density. It is density that the speed depends on, and it is because the more layers of atoms, the more interactions the photons need to pass through glass. But the interactions are elastic scattering. It is called the average time needed for an electromagnetic interaction.