Refactor textboxes so that they no longer extend L.Rectangle (i.e. eliminate the L.Rectangle outline so that textboxes are pure HTML wrapped in an instance of L.Marker).  Move DOM-specific code into a new class, Leaflet.Illustrate.Textbox.  Modify L.Illustrate.Create.Textbox and L.Illustrate.Edit.Textbox to extend L.Draw.SimpleShape instead of L.Draw.Rectangle.