First, what type of duck do you have?
I assume the typical frozen 'Long Island Duck' or Pekin duck.
Do not boil but do use your rotisserie.
For long and slow you need a low temperature (275F), somehitng that can be difficult to do depending on your Weber type? Do you use gas , charcoal or lump?
Lately we are getting a Mallard cross of about 4 #'s from the local farmer, and these are best cooked either in the oven, long and slow or the boneless breasts under high heat (425F) until the breast reaches about 115F and then rested for at least 15 minutes for a pink rare. the leg thighs are separately braised.
A fresh Muscovy is the prince of ducks for me!-Richard