I think I have an explanation for cosmological redshift similar to tired light, but without the need for photon-matter interactions.
The tired light solution needs photon-matter interactions (absorptions and re-emissions) to account for the tiny time delays that photons accumulate over distance.
But I think that the mere presence of matter particles is able to "slow down" photons, even when the particles do not interact with the photons directly.
The idea would be similar to that of the Huygens principle when applied to the double slit experiment:
In the double slit experiment, the photons that arrive at the final screen didn't interacted with the material of the wall where the slits are carved, yet the very presence of the wall modifies the way photons propagate through the space between the wall and the screen from then on. The atoms of the wall constrain the wavefronts that will develop by Huygens principle, changing how the photon will propagate in the free space between the wall and the screen.
The same thing happens every time a photon encounters a material obstacle in free space: if it is not absorbed by the particle, the way the photon will "explore" free space from then on will be different from the way that it would have spread if the obstacle hadn't been there. So the future evolution of a photon is affected every time it surpasses a possible detection, because it won't propagate the same as if the obstacle were not there.
After NOT INTERACTING with the obstacle, the photon wavefronts will interfere with themselves, like in the double slit experiment. The leading wavefront will be different from what it would have developed if matter were not present. The wavefront shape and properties change even when there's no interaction with the obstacle, just by the mere presence of the obstacle.
Imagine a photon coming to Earth from EGS8p7 (a galaxy more than 13.2 billion light years away). Every non-interaction with a matter particle in the interstellar medium (about 1 hidrogen atom per cubic centimeter) will add a tiny distortion and delay to that photon. Those effects would not exist if the interstellar medium were a true vacuum.
So, for me, it is not that space expands or the photon stretches as it travels through space: it is that the shape and properties of a photon change as it faces the myriad of atoms that reside in the intergalactic medium.
This is similar to running a billion double-slit experiments in a row. If a photon arrives at the final screen, it has interfered with itself for a billion times. Its spacetime properties (mainly frequency and energy) would be different than the ones for a photon that had travelled that same distance through free space undisturbed.
So matter particles constrain how photons behave, even when they do not interact directly. Matter presence "distorts" the photon wavefronts that develop next, creating a cumulative effect that can be measured over distance.
I think that cosmological redshift is caused by the presence of matter in the intergalactic medium, but not by a series of absorptions and re-emissions, but by a series of self-interferences caused, precisely, by averting matter interactions.