I'm just trying to explain how it works.
And I was offering suggestions to how the OPs problem might be improved.
I am not a color scientist, so my suggestions might be naive or impractical. If so, I'd like to understand why it is so.
Please, rethink it once again - how could we predict the original spectra of the scene, when countless different spectra can induce the same RGB signal?
How does a carpenter measure the length of a wall when the measure does not have infinite precision? He take the best reading that he can, make the best out of it, and (ideally) keeps a reference of the uncertainty.
How could we reproduce the original spectra using display that has a matrix with only three colour filters?
You use what you have to the best of your abilities.
A "rgb" camera or display may be seen as a somewhat irregular 3-channel filter bank (spectrally). By adjusting the gain of the 3 channels, you can get some level of approximation to some spectrum. If you had a 256-channel uniform filterbank, the _problem_ would not be fundamentally different (in my view), but the _precision_ of the reconstruction would be a lot better.
Think about it - even with e.g. 256 uniform spectral channels, there will still be limited spectral precision. You will still have ambiguity in that two different physical scenes can produce the same sampled signal (and thus impossible to separate or recreate accurately).
I am not convinced that the problem of the OP is really that the spectra are "hard" to record accurately (i.e. "hairy" spikes that can only be recorded using multi-spectral means, or at least color sensing aparatus that is a very good approximation to human visual perception). Rather, I have a feeling that the colors are (in a way) accurately recorded by his camera and representable by his display/printer. But somewhere along the line, our "best practice" color processing fails his task. By e.g. attempting to remove absolute WB. If "absolute scene white-point" could be established (by camera profile, or pointing a physical "white picker" towards the pastel sky), perhaps simple changes to color processing could attempt to make this the reference point (instead of "neutral white")?