(I'm not an astronomer)

I think for a 2D photo you just use the light you're getting. So the back of the galaxy is older than the front when you look at it. It's just a snapshot. The effect of the delay isn't that important, given the immense size of those bastards.

You'd only need the light from the front to the end of the galaxy if you were to create a full 3D-model of the galaxy... which is impossible because it would take several hundreds of thousands of years to create and some crazy algorithms to align all the light data to positions and trace them back through time...

Also, you misused "light years" in the first sentence, but the point got across anyway.