There is a full-page photo of a Remington Maynard alteration of an M 1816 on pages 32-33 of Echoes of Glory - Arms and Equipment of the Union.

I will have to consult Gluckman, Flayderman, etc. later this evening re specifics of changes between Types I, II and III, but offhand I don't believe there were changes to the bands themselves, only changes in the location of the springs or studs (i.e. in front of, or behind the band) that secured the bands.

Mike