Well, at the risk of being irreverently irrelevant, what about time dilation with repect to the life of a photon?
Consider a photon being sent from here to a point 4 lightyears away, on a course that will cause it to be reflected back (by a conveniently placed mirror) to its point of origen relatively speaking. The lucky little chap will have travelled for 8 years, (4 ly there, 4 ly back) we will have aged 8 years, the photon will have aged 8 years, and red shifted the approprate amount. Now if the photon has not aged 8 years, but only a few months, then for that photon, it only travelled a few light months. But then in that case the amount of red shift would not be a faithful measure of distance because it would be a measure of distance measured under time dilation and not otherwise.
Cheers,
Doug