Per the crushed blacks; the release print is several generations away from the color-timed negatives, and will have more degeneration in these sensitive areas (more blown highlights, crushed blacks).
The saturation problem is relative to the print screenshots you’re posting; you’re increasing the contrast to match the print, but you’re not lowering the saturation to match, which, relative to the print picture you’re posting, results in a over saturated image. As such, the algorithm is simply not accounting for this.
The release print is what creators intended to be seen. The low contrast interpositive was not intended to be seen by anyone, but the creators.
With regards to the saturation, being the creator of the algorithm, I can assure you, that the algorithm matches hue, brightness, and saturation. The print is more grainy, which may make it seem the regrades are more saturated, but this is definitely not the case. It is a mathematical certainty. Here’s an example for another high saturation print scan, that I used for a test a while ago:
35 mm reference:
Bluray:
Bluray matched to 35 mm frame:
It’s pretty obvious, that the algorithm has matched hue, brightness, and saturation.
I suggest you read through the thread dedicated to color matching and prediction: