The tired light theory is an interesting one, and I can see how it can fit well with observations. I like the tired light because it does seem to make the expanding universe less certain. Even the Big Bang becomes questionable and I see the CMBR as a possible detection of light that has given up the last of it's energy due to traveling too far.
I was more thinking about red-shifting accumulating due to the distance from the object. They always mention that further objects are more red-shifted due to them moving away from us faster. But if the red-shift accumulates over the distance due to more and more red-shifting coming from the expansion of space itself, then that doesn't tell us speed of the distant object, just the distance. I guess perhaps I always misunderstood what they meant by the red-shift being due to the objects traveling away from us. It's kind of a subtle difference perhaps. Does the red-shift happen at the point of departure of the object that is moving away from us due to the expansion, or does the red-shift happen during the journey from source to destination. Now that I write it out the first scenario makes little sense as different destinations would need to see different red-shifting amounts. I guess it would be: a) red-shift is due to the difference in speed, or b) red-shift is due to space stretching out underneath the light waves as the travel. Obviously the speed would have an additional effect or you could never see something blue-shifted due to it's actual motion relative to us.