I almost didn't reply, not seeing myself as learned in all this.
I haven't read any commentary from Tolkien on the original question but I think the evolution of the character of Gollum actually shapes the story. In TH, Gollum is almost a plot device, a weird creature who threatens Bilbo in a cave. The One Ring was written in after the fact to connect the story to that of LOTR.
But that connection ended up driving much of the story in LOTR. Gollum's finding of The Ring connects the story we read with the events of three thousand years before. The fact that Gollum was a Hobbit or "Of Hobbit-kind" is a graphic depiction of the effects of The Ring. Frodo's decision to spare Gollum sets up the ending of the story and it's ultimately Gollum who, "by chance if chance you call it", brings about the conclusion.