I don't think the OPs approach is quite right because it doesn't contain any information about numbers of photons, but it does seem to give a numerically similar answer.
The average energy of a photon in a cloud must be equal to the total energy of the cloud divided by the total number of...
...all the As and Bs should be A' and B' in the last line where I forgot to prime them. It wouldn't let me fix it afterwards - I did try. Sorry about that.
Don't forget that the wall is at a different angle to the x-axis and y-axis in the S frame than it is to the x' and y' axes in the S' frame too (due to Lorentz contraction along the y' axis).
You can work out the wall angles to the x-axis and y-axis as follows:
If the wall contains points...