Your suppositions in this passage are all unsupported. Huaxia emerged only during the Zhou. There were no Huaxia during the Shang. Dongyi also only emerged during the Zhou. There were no Dongyi during the Shang, and the Shang themselves were not Dongyi. In the Dongyi case it was also an exonym - the peoples referred to as Dongyi did not have a Dongyi identity nor did they call themselves Dongyi. Huaxia however was an endonym created by the elites of the Zhou states to describe themselves. It was not a tribe and there is no evidence whatsoever of a Huaxia under the Shang.
As for Liu Bang, there is no evidence that he was Dongyi/Nanman. His ancestors, according to the annotations of the Shiji, migrated to Xuzhou from Henan and were subjects of the State of Wei. You accuse others of mistaking cultural identities for race, yet here you are pretending Dongyi and Nanman are races when they were generic labels for peoples to the east and south of the Zhou and its inner vassals, pretending that Huaxia was a tribe when it was an elite identity among the Zhou states, etc.
I think you are overlooking the observations for which they are based. The Huaxia can be interpreted as being emergent from the rise of the Zhou but yet the rise of the Zhou also coincided with the rise of the Rong and Di. Obviously someone with pen and paper began taking into account all the people but it doesn't mean they weren't there before hand. Similarly for the Shang, of course they wouldn't call themselves Dongyi because when the term was invented the Shang were not in power but were forcefully laid alongside the Zhou. The Shang themselves looked to an ancestral claim from Dongyi regardless of who or where their noble house was actually later claimed to have been descended from.