Looking at the code for CharacterHandling, you can see that it does actually use Move():
var/destination = locate(last_x, last_y, last_z)
Move(destination)
Tsk, tsk. Naughty Deadron! =) It would seem that it's actually a bug in CharacterHandling. I'll contact him and tell him to fix it, but in the meantime, a temporary fix is to just edit the library yourself.
In my defense, there is a comment there that says "This doesn't do anything special if the mob movement fails."
I'll change the behavior and make a couple of tweaks to the library and update it today.
I'd like to improve it to make it easier to provide your own UI...however, if you specify that a player only gets one character, everything just happens automatically. In that case I believe there is no UI.