Schönberg did not compose anything worthwhile after his 1908 string 4tette, and certainly he could not be said any longer to be a "composer" by the time he reached the Americas. Nor do I think there have ever been any really worthwhile native composers in that part of the world.
I can't agree with you on any of these points. In fact, Schönberg did his best work after 1908. He is also a significant German song composer, comparable to Wolf, Richard Strauss; maybe not quite in the same league as Mahler.
Native Americans are American Indians as far as I know! George Crumb is an excellent example of an American composer who could easily cross the Atlantic. If you are into modern music, there are whole channels on YouTube of similarly talented American composers. Not many countries around the world have generations of great composers. Austria, Germany that's about it. America has a recent history and a fair share.