Endless rumination about the 'true nature' of a quantum of light is a waste of time. As a visually-oriented person, I'm prone to that. To quote a famous piece of doggerel,
"The man behind the microscope,
Has this advice for you:
Don't ask what it is;
Just ask what does it do?"
That said, I'll interpret "tired" to mean red-shifted, for the sake of internal consistency. Although I'm not a physicist, I know of three mechanisms by which a photon can become red-shifted.
1. Ordinary Doppler redshift
2. Special Relativity redshift. An observer/passenger on a high-speed train points a portable laser out the window. His measurement of the laser light's wavelength will be slightly less than that of a stationary observer standing to the side of the railroad tracks. Of course, I'm assuming arbitrarily accurate measurements on the part of both observers.
3. General Relativity redshift, aka gravitational redshift. A photon escaping the gravity well of a massive star will be red-shifted slightly. More precisely, the spectral 'lines' of that star would appear to red-shifted, relative to those of a smaller star.