You are in the wrong game then. I can make any model work if I don't care about the details. It's getting the details right that's a pain.
You understanding is wrong. The way that the standard model handles electron recombination is exactly the same as how the Milne model does.
So can you with the Milne model calculate the exact spectrum of the lumpiness. With lamba-CDM, I can put in some parameters and get a fit to get the lumpiness.
Can you do that?