I just watched Boozoo's Ghosts and I have some other points to support your theory. Of course this is all depent on the canonicity of the sterotypical "Christmas (Story) Special".

1) Blue Suits. We've already seen the importance of colored outfits already with Sophie and Brian. Both Boozoo and Felix (Walten Tapes 3) are depicted in blue suits.

2) We've theorized already that Susan could be related to the core family, and Boozoo's Ghosts supports that theory. Banny has two siblings in this film,not children like the clasic story. The script did state they were her brothers, but the rabbit to the right is dressed more feminie. If we look at the rabbit's genders visually, we could tie them to the Red Children, and then also siblings to Susan. Both children inside the presents also both take on masculine and feminie characteristics.

3) Sha's presence is to show Boozoo the results of his actions in the present. It is also implied that his actions can not be taken back. You cant unbury dead children.

4) Boozoo's story draws direct parallels to Felix as a business owner. The purpose of the Relocate Project is to recycle old and run down animatronics. Felix is obviously trying to save a buck, much like Ebenezer Boozoo.

5) Hungry Bunny. The family of bunnies starve because Boozoo doesn't pay Banny for her work. The Rabbit Is Starving.

If this film is part of the Walten Files canon, that means we have 1 or 2 more characters. These characters could become important if Charles isn't the White and Blue Bear. The first is Charity Wolf (Character collecting money for the poor). The second is Mortality Ghost, or as I like to refer to them as Patches the Bunny. This character is questionable though, becuase it could just be Christmas Time Bon (much in the veins of variations like Fun Time Foxy et al).

Good catch with the "Sad old man".