Lumping them together is your prerogative, Phil. Chantying has to be a subgenre of maritime worksong. It's just that most of us prefer to concentrate on the chantying itself and the direct precursers with a known connection.
Whatever Wallack was doing it surely must be based on something he had seen, not necessarily in the RN. As far as I'm concerned I'm happy to accept that some chantying was happening in the 1820s in anglophone vessels. We need to find more evidence. All of the 1820s and earlier evidence needs pulling together.