"does it make Kiev Russian ?"
- here I didn’t understand what was supposed to make Kiev Russian, if it was already the capital of Russia(Rus')? By the way, Kyiv began to lose its importance even before the arrival of the Mongols. After him, the Vladimir principality, and then the Moscow principality, began to raise its importance.
"What about the history of the intervening centuries, when Kievan history and culture evolved separately from Moscow ?"
- yes it was. from 1240 till 1654. but even at that time they called themselves Russians, Rusyns, Rusichs.
The ancient Russian state was formed in the 9th century near Novgorod. Then it captured Kiev and began to grow at the expense of the nearest tribes. All this was a Russian state (Rus'), consisting of different principalities, which often even fought with each other.
And the inhabitants of these principalities were Russians (Rusichi). And when the inhabitants of present-day Ukraine came under the control of Lithuania, they also remained Russians. That state was fully called "The Grand Lithuanian, Russian and Zhemoytskoe Duchy".
When Hetman Khmelnytsky decided to reunite these lands with Russia, they called themselves Russians, Little Russians, the Russian people. It's all is in the documents.