I forgot to mention that this is also how Hector Duhon and Octa Clark played. On that old album with the black and white cover, they have Michael Doucet playing guitar but you can tell they don't need him. Hector does some really interesting things playing around the melody, weaving in and out, but what he plays is mostly based on the melody.
We haven’t crossed that bridge yet because she hasn’t sung anything. I guess I would keep the rhythm going with the bass and use two or three note chords in the right hand, with some omissions where the bass and chord would clash.