I took 'embed' to mean that if you have an existing drop-down menu, you can add a button with FileType NEWMENU to add the "new" menu items to the same menu.
However I get an additional level:
Have I misunderstood the help?
I'm using this in the Lister Context Menu as shown:
I don't think there is a way to add just the contents of the New menu without adding the New menu/parent itself at the moment.
(We usually have buttons for the few types we need often at the top level, then the New menu as an "other" sub-menu, keeping the other items out of the way.)
I haven't looked at the code yet but it should probably be possible to change it to provide a way to do what you want.