Tiny update:

While I’m still not really sure how to go about recreating the filmic look, I’ve discovered something quite valuable to the progression of this project. Before the theatrical release, Paramount released several high quality renders of stills from the movie to the marketing department for the German release of the film, to use for lobby cards and other general advertising. These were released publicly on December twelfth of 2004. Note that this was still several months before the first official home release. There is enough evidence to suggest that the movie’s palette was indeed changed to a noticeable degree, likely to more closely match the fourth season that was airing in between the theatrical and home releases. You can see this in one comparison here:

German publicity photo:

2011 Blu-ray (my own copy)

I could be wrong about the origins of the publicity photo, but until then I’ll take it into consideration as a reliable color source