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.