> I had year long discussion about similar topic by email, so I see nothing exceptional there.

But the point is we have models which predict quite specific values for the angular power spectrum, and when compared matches observations very well.

This is highly non-trivial. And for any new model to take over, it must do better.

It's not enough that it has potential to have some sinusoidal-like features. Lacking matching model predictions, you'd need to have a plausible explanation for why the features are missing from your model predictions. For example you used some first-order approximation for some term and due to <insert convincing argument here> a higher-order approximation should produce the missing features.