A large image travel distance would have a large distance change due to a specific time variation.

A smaller image travel distance would have a smaller distance change due to the same time variation.

Red and blue shifts can be caused by velocities also.

The total red or blue shift will be a combination of all causes.

The expectd result would be a red or blue shift proportional to the aparent distance an object is from the observer.

Which is what we observe.

I can show you some simple calculations if you wish.

Duane