Hmm.
"..tell me where I've gone astray."
You need to heed Braggs advice "its not new facts but the way we think about facts that's important", and Einsteins; "We can't solve our problems with the same way of thinking that created them". Take a step back and re think;
"photons are both emitted and absorbed with velocity c."
Imagine a person has a rocket bike, and the fine structure boundary electrons of his eyes. If he is at rest, the electron will both receive and emitt the photon at 'c'. (on the same vector - as HFP) so the signal is passed into his eye at 'c'. However;
If he then shoots off on his bike towards the source, the photons will be absorbed at c v, but still emitted into his eye at 'c'. He therefore sees them at 'c', but Doppler shifted.
If he heads away from the source, they'll be absobed at c - v, but still of course emitted at 'c'. So he sees them at 'c', but further apart (red shifted).
That is exactly how Frequency Modulation works. The wavelength is altered back to the original by a preset oscillator frequency, emitting at 'c' whatever relative speed the signal is absorbed at!
The fine structure (constant at rest) electrons of measuring instruments does exactly the same.
That's how energy and frequency are conserved in Huygens Principle and Fourier Optics - by changing the speed and wavelength, refracting the wavefront angle.
Ergo; CSL is explained with a quantum process, unifying physics and removing all the paradox from Special Relativity.
If you still dont see it, take Bragg and Einsteins advice; Clear your mind of preconception, take 3 steps back in your mind for a better 'overview' and visualise it, picture it in your mind, as you read through it again really slowly.
Does that work?
Peter