Ultimately, your legitimately-registered votes need not answer to anyone but yourself. If you believe that an answer to a frequent duplicate is "Not helpful", then down voting would seem to meet the spirit of that feature's intent.
Two things come to mind, though;
First, the votes probably won't have the effect you want without doing what you did on the question you link: Commenting why you down voted. But I'm not convinced such a comment/down vote will accomplish your goal. In the case of some folks, it may encourage them to do the exact opposite.
Second, questions that are duplicates are eligible to be merged, for the situation where a duplicate receives good answers and the 'original' question seems canonical enough. So, the system was designed for this to happen.
I don't think I would do this, myself. Duplicates will happen, and people posting answers won't always have any clue a duplicate existed. Often, a duplicate might get a better answer than the 'original' ever did - which I expect is why the 'merge' option exists for mods.
I would simply mark the post as a duplicate, and leave it at that. Don't up vote any of the answers.