I agree with this analysis, mostly.
However, I believe there's more in it than you may realize.
LOTR was written by a man who was born and grew up at the height of Western Civilization's self-confidence. His stories display an ultimate faith in the worth of the civilization and its ideals, no matter how often those ideals fail to be achieved.
In the movies that is best shown by Sam's great speech about some things being worth fighting for.
Martin has obviously, at least to me, been brought up in the cynicism of our present elite. The book is not about a battle between Good and Evil, or a battle between civilizations, it's about a squalid struggle for power within a civilization. To Martin, and people like him, that's all that is Real. The relevant point is not whether they are right or not, it's that their perception is to them all that exists.
So to me, GoT is based on the modern liberal worldview, LOTR is based on the older worldview held by many conservatives.
Note that I have seen only segments of the GOT series, and read only about the first three books in the GOT series, and that was a long time ago, so I may not be entirely accurate in this charactierization. OTOH, I know Tolkien inside-out.
Excellent observations, Sherman Logan.