You
do like Immanuel Kant, don't you
Nog?
I just want to point out that things like "Void" and "Ainulindale" can also be quantitative (if i got your definition right), in the sense that there is lots of music but none as grand as Ainulindale, or spaces with little in them but the Void is the most empty of all of them. You can quantify such things not only by their innate qualities but by an event or role they play or etc. There is an infinite number of categories you can look at. You can also say that things existed for a long time, but the Void is the oldest still - which also gives it a quantitative "extraordinariness".
Personally, I'm not enthralled with the people/living beings, because there's too much to argue about regarding who is greater/stronger/taller/etc. So out go Arwen, Isildur, and Thuringwethil. Then, despite its importance to the story and unique quality, I'm not a big fan of Melian's Girdle. It just doesn't seem to do it. Neither does the Void or Gondolin. Just not the right ring, ya know. I think Lembas and Mithril can have a silly side to them as well as the radical reasoning of why they are extraordinary, so they would be pretty high on my list. Music of the Ainur is quite fitting by definition, and it resonates with me, so had I been the judge I would have considered it. And the Green Dragon is comically true, since, as Mr. Sandyman was quick to notice, "there is only one Dragon in Bywater, and that's Green".
So, for my money, mithril, lembas, Music of the Ainur, and Green Dragon are worth consideration.