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I also figured out the rest of the bass part (although I might have a few notes in the wrong rhythm) and a very small part of the horn part (I think it's trumpet), which - since it's doubled on piano (in the first verse at least) - I played on piano.
In learning how to play the parts, I split the stereo track from The Decca Stereo Anthology. It's mixed sort of oddly in that the left track is the vocals and the overdubbed session musicians (vibes, brass, and some percussion [I don't think I ever really noticed the timpani]) and the right is the vocals and the Zombies' normal instrumental ensemble. It results in some parts of the left track that are more or less a cappella, which is really interesting to listen to.