While I'm not as familiar with NYC heavyweight passenger cars, whether the car was lettered for the railroad name or for the Pullman Company depended on the configuration of the car. Typically dining and sleeping cars were lettered for Pullman as they had a monopoly on providing those services to the railroads. While I should be familiar with the configuration of the GGD observation, the floor plan escapes me now. Many long distance observations had multiple bedrooms and typically a rear lounge. Those would be lettered for the Pullman Company. If the observation was all coach seating then typically it would be lettered for the railroad.
I know it's not the definitive answer you are looking for, but at least it's a start?
Looking forward to seeing your whole train!
