As you linked to Lorentz contraction I assume that you are asking how relative speed, and invariant mass can 'distort' the photons 'propagation' in 'space'?

And that you also expect it to be visual aberration maybe? As seen through the 'lens of gravity' as you discuss it as a 'delay'?

There is never any 'delay' for a photon or a wave as I know. It's as fast as it can be under whatever cases circumstancing/'limiting' it. In a chilled BOSE condensate you might assume that it is 'stopped' and so 'delayed' infinitely, but it's light, and light have only one speed in a vacuum. So when you find it taking the 'longer path', bending as seen from us, it just describes the shortest path possible in SpaceTime. Or you can look at as all other paths would cost it 'energy' to take, which in fact is a impossibility for a photon to do, as far as I know? Photons do not expend 'energy', except in a interaction annihilating it. And when it comes to waves I think it has to be the same?

Then the effect a space pilot see in a Lorentz contraction, telling him the distance to his goal, has to be a lie too, right? But as he can measure his speed as near 'c', what then makes him reach that goal so much faster? He can measure his time and find it to be the same as always. In fact there is no way for anyone to change his rate of time as observed inside his own frame of reference. So to assume that position, you will need to invalidate all experiments done in that frame of reference. And that goes directly against how we test and experiment.

Assume that he moves uniformly after accelerating. Will he still see a Lorentz contraction? Yes he will. Can he now do the exact same tests with the exact same outcome as any other uniformly moving rocket/object (ignoring tidal forces) ? Yes he can.

Does their relative speed versus each other or some common origin change that? No it doesn't.

Will their time then be 'the same' as they all get the same results? Yes, I can't see any way around that assumption myself?

But they will still have different Lorentz contractions then? Yes, they will..

So a Lorentz contraction is 'real'. As real as a 'red' or 'blue' shift.

It's all relations

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(What I can say about it though, is that all those weird things with light makes me more and more to think of it as not 'propagating'

It's just too many weird things about light. If it was a 'constant' instead, defined through interactions, and the relations surrounding those, then it would be easier to understand for me. As it is, it gives me headaches.)