When will you realise that there is no "lack of continuity" for Gollum, that Gollum's Pity theme is one of the cornerstones of the score?
Plus, neither song was meant to have any influence on the score. The score tells the story of the films, and when the credits roll, the music is finished telling a story. It's quite simple really, don't you think?
In any case, you can't say the music for Gollum lacks continuity merely because you would have liked to see Gollum''s Song to reappear, which was not done with clear intentions.