We live in the age of measurements and observations and specific mathematical theories that fit measurements and observations beyond any doubt.
Photons are elementary particles. . They have zero mass, and other characteristics which separate them from other elementary particles .
Can photons lose a small amount of energy over time when traveling large distances due to either weak interactions with magnetic fields (Faraday Effect)
This is an electromagnetic vertex for a photon, the faraday effect is for the emergent light beam from innumerable photons.
or due to the way all objects cool and give off thermal radiation (Second law of Thermodynamics)
No elementary particles behave thermodynamically. Thermodynamics is an emergent theory over many particles (statistical mechanics). Energy is gained or lost through interactions.
or gravitational interaction with nearby dust particles?
gravitational interactions with a strong gravity well, yes. Dust particles do not have enough gravitational potential for a measurable difference.
In all cases the photon would lose energy by interacting randomly. Random interactions would destroy the spectra coming from stars and galaxies that show a redshift, (loss of energy). After all it is from the displacement of spectral lines of known atoms that the study of observational astronomy took off.
That the universe is expanding we know from measurements of the velocities of clusters of galaxies. None are moving towards us. They are all moving away, and the raisin bread analogy might give an intuition how this can happen.
So the time when one could think up alternate models for the universe by handwaving is long gone. One needs hard measurements and concise mathematical models.