NGC only uses the multi coin holder now for some bulk submissions from authorized dealers. Individual members can't get them anymore and haven't since 2011.
That's a different situation. Depending on the coin, it would probably be better to break it out and have it slabbed. A toned coin enthusiast would probably not care about the other coins in the set.
coins in pcgs slabs that are errors do command, and get more $$, this is why i tend to avoid them, but dismantling this set would be a grievous error in my opinion, as per others already stating the fact, an existing govt' set with an error is quite rare to find.. and you will save 30-50 dollars having it graded...very nice coin, by the way, and nice find...