Firstly I think it was the Voodoo Priest who did the doll and not LeChuck. Also, Largo has been tailing Guybrush presumably for much of the game though he never steps in to stop Guybrush getting the map-pieces for some reason.
Maybe he bought the plaque that had Guybrush's spit on it from the antique store, got his dress from the bushes on Booty Island. So that's thread and body.
The head part is a bit of a mystery though.