Now, almost ten years later, I have found another group with a similar aesthetic called The Original Danish Polcalypso Orhestra, also known as Karlekammeret. Interestingly, Karlekammeret released their first album of Caribbean inspired traditional music in 1989, right around the time when the Etcetera String Band would have been recording and putting out Bonne Humeur. Something must have been in the air connecting Copenhagen to Kansas City!
The Original Danish Polcalypso Orchestra's approach was a little different, in that they primarily mimicked the instrumentation of St. Croix Quelbe or Scratch bands like Blinky and the Roadmasters or, more importantly, James Brewster's bands such as Jamsie and the Happy Seven or Jamesie and the All-Stars. The Scratch music of U.S. Virgin Islands does often have vocals, it's not all instrumental, but when soloing the head melody lines are usually played instrumentally by a saxophonist. Karlekammeret also had a banjo-mandolin (or maybe banjo-ukulele) but its role was primarily rhythm rather than lead melody as in the Etcetera String Band.
Being saxophone-oriented, the recordings by The Original Danish Polcalypso Orchestra tend to be in the saxophone friendly keys of Eb or Bb, whereas on Bonne Humeur the Etcetera String Band plays most of their tunes in the mandolin friendly keys of G and D. There actually seems to be one song that was common to both band's repertoire's and that is Sam Polo, a West Indian bamboula, although the arrangements are different.
The Etcetera String Band never did a followup to Bonne Humeur and I've often wondered what pieces they might have included if they had done a sequel? With the recordings of The Original Danish Polcalypso Orchestra, it seems that there may be a possible answer to that question!