I've also been thinking about the "Yamato" thing. I've seen English language sources claim that Yamato and Daito are alternate readings. But the famous "Yamato" as in the historical Japanese people is not 大東/"big east," it is 大和/"big Japanese," correct? (ie the one with "Daiwa" onyomi)
The original ancient name for Yamato was written as 倭. I gather that this was the name used by Chinese and Koreans to refer to Japan. Then under the Empress Genmei (707-715), the characters were changed to 大和. Or so my university students tell me. They are not aware of 大東 as a name for Yamato.