Thanks for the suggestions. I actually found a way that, while an elegant solution for me, might not be the best for others, but I figured I'd document it here.
The short of it is that I am already heavily utilizing functions in my game (because you always should), so the PlayerFamily picks the appropriate MountFamily in this case, then passes that MountFamily objects UID to a function that identifies the MountFamily by its UID.
However this function instead picks the MountFamily AS a PlayerFamily (remember, all Mounts are Players, but not all Players are Mounts) giving me access to all of the PlayerFamily functionality I already have setup.
It would maybe be a little cumbersome on its own, but this baton pass approach easily fits into my heavy use of functions already, so it worked very naturally for my project.