I think some of the early baroque music written in the 16th / 17th century for theorbo would perfectly adapt to the stick. Both stringed instruments share the idea of combining the guitar (lute) and bass range, whereas the theorbo has unfretted open (and very long) bourdon strings.
Solo music for theorbo was written by e.g. Kapsberger, Piccinini, DeVisee (also Bach for archlute) and often features a melody voice with a (counterpoint) bass line.
When I got my new N/S stick I will explore more on this