The best course is to checkmate directly without toying with the opponent, however obstinate. If he wants to play it out to mate, that's his right - you cannot be forced to resign under the rules. Just get it over with and move on.
In games among weak players, multiple Queens are not uncommon, but they are fairly rare at the higher levels of strength. One exception comes to mind: Bogoljubov-Alekhine, Hastings 1922. Alekhine sacrificed his Queen to promote a pawn a couple of times; when he gave up his third Queen to force promoting to his fourth, Bogoljubov resigned. Probably one of the 20 best games of all time.
While this is true its equally true that noone can be forced to deliver mate as quickly as possible. Good players rarely ever continue when their position is hopeless.
While it may not be unsportsman like; it is usually a great waste of time. I much prefer to start another game. On occasion I have resigned from the stronger side when playing an off hand game; I mean the poor bloke must be in a desperate need for a win to play on. In tournaments I try to finish off my opponent as expidetiously as possible in order to conserve resting time before the next round.