I honestly think The Fellowship of the Ring would start with Frodo waking up shortly after destroying the One Ring as seen in The Return of the King, then the scene would change to the beginning at Bilbo's birthday. I also think the movies would constantly show backshots of the characters. I also think The Return of the King would end with Frodo waking up travelling to leave Middle-earth, later he'd check if his adventures were a dream somehow, and would be visted by Sam, Rosy and their children and the final shot of the movie would show the book Frodo was writing