We have slightly different models. You've obviously put more thought into yours, but I still like mine better, though I entirely admit I haven't studied the implications of either.

Your model challenges two fundamental assumptions, and mine only does one.

For my model, the speed of light remains constant, but the energy of the photon decreases as it travels. A photon is a car fueled with itself, slowly burning itself up, though I'm not committed to it entirely burning itself up in the limit.

I wouldn't think this would have anything to do with "dust". Just travel through free space. I'm not explaining the effect, which I'd guess would require general relativity, just noting it as a possible mechanism for the observed red shift.

La Wik:

Following after Zwicky in 1935, Edwin Hubble and Richard Tolman compared recessional redshift with a non-recessional one, writing that they:
... both incline to the opinion, however, that if the red-shift is not due to recessional motion, its explanation will probably involve some quite new physical principles [... and] use of a static Einstein model of the universe, combined with the assumption that the photons emitted by a nebula lose energy on their journey to the observer by some unknown effect, which is linear with distance, and which leads to a decrease in frequency, without appreciable transverse deflection.[16]

Sounds about right to me.