I think Barty and Bill should have an adventure together. Not because it would add to the emotional arc of the fic in any significant way but because I think it would be really funny (and I'm so enchanted with the idea of Barty, for a character that only appears in a handful of chapters haha)
So far Bill doesn't know Barty is a person. He just hasn't happened to notice him. He hangs out in the kids' room and he usually isn't moving, Bill's never registered his existence.
I don't know when, I don't know how, but somehow Bill's going to find out about Barty and be utterly mortified that there was a whole extra person in the Mystery Shack that he just DIDN'T NOTICE.