I address that point in the notebook. Thanks to Fourier you could decompose any waveform, coherent or not, into a sum (integral really) of sine waves. So the lack of coherence should not make no difference to the argument.
Therefore the "coherence answer" is exactly and precisely the correct one. What you are doing is simply explaining it with different words. "The lack of coherence" of the wave as a whole is THE argument.
What your explanation is doing is applying a narrow wavelength filter and evaluating the conditions for each \Delta\lambda, which is absolutely a valid approach, but it is the same thing. Overall I like your explanation very much, but please be careful about statements like "not really the answer, at least not directly" as they only point at a misunderstanding of the coherence explanation.
The correct answer to what question?
If the question is why we don't see iridiscence when "white" light (wavelength 380-740nm) is reflected on a "wide" film (several orders of magnitude larger than the wavelength), do you really need to talk about lack of coherence? The fact that for a particular width the film will supress/enhance thousands or millions of colors across the visible spectrum should be enough to make the resulting light white as far as human perception is concerned, I think.