I was curious on what values were adjusted for the LUT (Look-Up Table). Not knowing how this is implemented, my hope was that it was analog in nature (dimmer/brighter light source with shorter/longer exposure) and not digital in nature (like a paint program's rounding-error-cascading integer math).
FLAT CAPTURE
First was to stretch out each R-G-B spectrum from it's fade-compressed range to a full range (0 thru 255). This I expect to be the proper approach for correcting faded film, which loses it's contrast in becoming ever more transparent. Note: the sample should have a full range of color for greatest accuracy of color correction -- which I ignored for this test.
R-G-B NORMALIZED
RED 12-166 to 0-255
GREEN 4-176 to 0-255
BLUE 4-170 to 0-255 LUT CAPTURE
Clearly, normalization wasn't the approach use for the LUT capture. The LUT capture didn't have the white cartoon teeth that normalization produced. A quick search revealed that gamma was the adjustment for look-up tables in graphics. So, next, the range was left untouched in favor of gamma adjustment. This came close but it also required midtone adjustment for a better match:
R-G-B GAMMA & MIDTONE ADJUSTMENT
RED 1.5 & -15
GREEN 1.3 & -4
BLUE 1.2 & -3 LUT CAPTURE
Of course, I don't know how you determined what settings to use for the LUT to pull as much color out of the faded film as possible. Was it from a known movie reference or by a general standard of adjustment?
Here's something interesting. Clinging to my film fade contrast approach, what if normalization was a missing factor needed with the gamma & midtone adjustments? Combining the two sets of values produced this:
I'll test this idea on the coach scene with real people. If this works well, the master color correction might be performed in the analog capture (if possible to make such adjustments), with only minor touch-ups made digitally thereafter.