Well yeeeees, it
is a single word, but it's a compund word, no? As you say, "extra" meaning "outside of" and ordinary(-rius) "Of or relating to order; orderly, usual, customary, regular, ordinary." So, outside of the norm, pretty much.
Having said that, I still say ek-straw-din-airy, but that's because I'm an oik.
Discussing pronunciation is one thing, arguing about "correct" pronunciation is never going to end well. We speak "the queen's English" - this from a woman who can rhyme "house" with "rice."
Oh, er - better bung in a smiley in case I've been accidentally inflammatory