>because there is a very real difference from a photon going from the Sun to the Earth, to a photon going from the Sun to Jupiter.

Not from the photon's point of view. This is very crucial and it is not because of notation or maths. The real difference is from your point of view. I know it's counter-intuitive but that's different from being useless.

Sun->Earth or Sun->Jupiter is a small beer. It is the same for photons from the CMB being recorded. For them, they have been emitted and absorbed at the same instant and experienced no passage of time or distance traveled