That’s a lot of great work! (I hadn’t heard of Levenberg-Marquardt before, only the distinct Gauss-Newton and Gradient Descent algorithms that it interpolates between. That’s a clever way to get some of the benefits of both methods.)
I wouldn’t solve the kind of discrepancy you pointed out in the gray swatch by boosting the whole channel uniformly. Instead, I’d solve it with a calibrated 3D LUT. That’s exactly what that particular tool is for and it defeats the problem perfectly.
This does push the problem back to getting your hands on a calibrated 3D LUT in the first place though.
Kodachrome calibration targets are no longer available, which makes me wonder how far off any target printed using a three-dye system would be vs. a Kodachrome target. Certainly, every three-dye film stock will exhibit the same wavy characteristics for the same reasons that Kodachrome does. So, if the same dye curves are available for other stocks, I’d be curious to see how far off they were from one another. More specifically: my calibrated 3D LUT comes from an Ektachrome target with 288 swatches. How far off would some hypothetical simulated Ektachrome curves be from your simulated Kodachrome curves?
I’m willing to bet they’d be a lot closer to one another than either is to the reference color checker line. A comparison between those two in particular might highlight the worst metamerisms to keep an eye out for, too. That would be useful information.
If it turns out they’re very close to one another, a calibration obtained for one film stock could be considered valid (within some threshold or, say, with the caveat of a problematic metamerism or two) for the other. Knowing that threshold (vs. other film stocks, too) would be cool because Ektachrome calibration targets are still available.
Another detail: it’s useful to remember we’re not taking point samples on these curves. “Narrowband”–at least, until you’re using lasers or adding bandpass filters–isn’t necessarily as narrow as it sounds. Recall my measurements where each LED had a bandwidth between 30 to 40nm. Taking the extra bandwidth into account doesn’t solve the problem, but it would soften it a bit on average.