Peter, my memory of it is this.

The bass lines starts first. Get the audience to sing it comfortably.

Then the tenor line which is kind of the melody of the song. (Not including what's being sung over it).

Then the alto line matches the tenor line a third above.

There are essentially three parts. The bass is singing "way up oh, wimoweh" or something approximating and English bastardization of African.

The tenor is singing "wimoweh, wimoweh, wimoweh, wimoweh"
and the alto sings the same lyric a third higher. The soprano part might want to double the tenor.

Once the bass is secure, than add the other two parts and you sing over it.

Frank Hamilton