I need to get these missing songs back on to their original playlists.

Correct. When you press "down down down" on the player's front panel, you are playing all playlists, not all tracks. If a song is not in a playlist, it will not show up in that shuffle.

A discussion of the difference between the playlists and the soup is here.

Another solution would be to use JEmplode to create "soup playlists". It's a new feature in JEmplode. Recent beta versions allow you to automatically create playlists based on the soup.

I can obviously copy them but will this be duplicating as the files are still there!?!

Depends on how you do it. Please click here for the details.