Azzam
The train paradox evaporates when optics is used from the text books. There may be an analogy with your vacuum energy, because Doppler shift is also an energy shift. Perhaps you could see how close your mathematical solution comes to describing this underlying physical explanation, which has 100% logic and experimental proof.
In the rest frame of the train, light from the flashes front and rear enters the glass screens, does c/n (n=1.55) in the glass, re enters the air and does c/n in air (n=1.0003) or c in the vacuum (n=1) so in a short time both reach the observer sitting at the centre of the train simultaneously. All childs play OK?
The light from the flashes also heads towards the observer at rest half way between them on the embankment. It does c/n wrt the air (or c in vacuum), so a short time later also arrive at the observer simultaneously. Equally childs play Yes?
But do both observers see the flashes simultaneously. Of course they do. But during propagation the observer in the train has moved with the train slightly, so is of course no longer precisely opposite the other observer. No problem.
So do they see each other light up simultaneously? Yes, slightly after they themselves are lit up due again to the propagation time from one to the other.
So where than is the paradox? Why do we need length contraction and time dilation??? The contraction and dilation of energy (wavelength) is the Doppler shift of the signals in the train implemented at the windscreens, because they re-emit light at c wrt themselves. So the light from ahead is seen by the train observer blue shifted, and the light from behind red shifted, affecting energy, but of the light itself, not somehow of 'the vacuum'.
Can you find any error of simple logic and the laws of optics in that solution? Agreed, both SR and QM are better interpreted, and consistent.
Peter