Just to add a little to this.

"L'Année Passée" may well have been a folk song that was copyrighted by Belasco rather than an original composition. The first half of the 20th C was a land grab where many folk songs were appropriated.

"Rum and Coca Cola" was definitely written by Invader.

The two share a tune, but this is quite a common calypso melody. "Man Smart, Woman Smarter" is probably the best known of the songs with a related melody. "Blue Tail Fly" by the Roaring Lion is another (not to be confused with the American folk song of the same name).

The bamboo lyrics come from another song, "Big Bamboo". There are two versions of this song. One, originally by the Duke of Iron (I believe), has an unrelated tune. The best known recording of this version is by Lord Creator. The other version is more popular with Jamaican mento bands and ends 'la-la-la, working for the Yankee Dollar'. This version has a very similar melody to "Rum and Coca Cola" etc. and was probably influenced by that song.