To be honest, the scouring is one of my favorite bits because it shows how much the main hobbits have grown over the course of their adventure. I think the multiple endings thing worked better in the book for multiple reasons. For one, you could tell at any time that there was still a considerable chunk left to go, so the narrative didn't create any false expectation that it was about to end. But also, unlike in the movie where it does the usual swelling soundtrack and post-climax wrap-up like it's about to finish but then just continues and does it again, I feel like the book doesn't do a literary equivalent of that at all. It doesn't feel like multiple endings, but rather multiple conclusions to separate story arcs, which is something the books do all throughout. The book is just forced to cram several right at the end, because it has to finish somehow. It's unfortunate that the structure didn't translate well to the big screen, at least not without cutting things out.

I'm not totally convinced but it's been a long time since I've read the books and at least accept that a book is better able to weave together multiple threads and story arcs than a film easily can.