fundamentals all the way down
It's possible to imagine Antarctic world domination, but if it were concretely possible to realize Antarctic world domination, then perhaps we would be under the domination of Antarctica. Put abstractly: Any concept of exceptionality presumes ordering principles that make the world a world at all, the universe a universe at all, or comprehensible at all as other than a chaos of equally unique, indifferently different events.
I'm having some difficulty putting your other criticisms together with their origins, but, in general, I don't see a problem with the exceptionality or exceptionalisms we discuss as being both fundamental and subject to change or loss, since even fundamentals are subject to change, or are always merely relatively fundamental from some next higher level of abstraction.
On the exceptionality question, the banal facts of long coastlines communicating with the two major oceans, on a relatively easily traversable yet vast and, again, relatively thinly populated, mostly temperate and resource-rich interior, will continue to matter very much, as far as the practical requirements of trade, warfare, and economic development go. At the point, whether through technological advances or cataclysm, that this all is no longer exceptionally important to a real-existing human species and its real-existing capacities, then the era of American exceptionality would be over, but probably not before.
As for types of exceptionalism, the considerations are more complex, since they will rest on different theories of human collective agency. It's an adapt/adopt variant of the usual chickens and eggs: Did we adopt a liberal-democratic political culture because liberal-democracy proved adaptive for us, or have we managed to adapt because we adopted liberal democracy?
Yes, I believe that's clearly correct. The term "New World," which precedes the European naming of the continents, also already begins to convey something quite profoundly exceptional. So, originally, a study of American exceptionalism could start as an analysis of all of the ways that occupying a New World would tend to differ from occupying the Old World. A true exceptionality would be conceptually prior to whatever exceptionalisms.