score:15
Short Answer
It appears that some liberties have been taken with the etymology of βάρβαρος in the sources you have cited. Not until the Roman period do we have a suggestion of an onomatopoeic origin (in Strabo, died circa. AD 24) for barbaroi. Classical authors do not make this connection, though they do compare (and often make fun of) 'barbarian' languages with reference to certain animal sounds. Modern scholarship tends to emphasise the possible or likely Sumerian origin of the word barbaroi.
Details
The English translation of Strabo's Geographica or Geography, suggest that he was not 100% sure, and Strabo does not directly refer to a particular writer from the archaic or classical periods. The translation below is from the Loeb edition.
I suppose that the word "barbarian" was at first uttered onomatopoetically in reference to people who enunciated words only with difficulty and talked harshly and raucously, like our words "battarizein," "traulizein," and "psellizein";57 for we are by nature very much inclined to denote sounds by words that sound like them, on account of their h*m*geneity. Wherefore onomatopoetic words abound in our language, as, for example, "celaryzein," and also "clangê," "psophos," "boê," and "crotos,"58 most of which are by now used in their proper sense. Accordingly, when all who pronounced words thickly were being called barbarians onomatopoetically, it appeared that the pronunciations of all alien races were likewise thick, I mean of those that were not Greek. Those, therefore, they called barbarians in the special sense of the term, at first derisively, meaning that they pronounced words thickly or harshly; and then we misused the word as a general ethnic term, thus making a logical distinction between the Greeks and all other race.
57. Meaning respectively, "stutter," "lisp," and "speak falteringly." 58. Meaning respectively, "gurgle," "clang," "empty sound," "outcry," and "rattling noise."
A more recent translation (2014) differs very little from the above, using 'I think' instead of 'I suppose'. There are few uses of barbaroi (or related words) in archaic literature (just once in Homer) while, in the classcical period, Herodotus makes it clear that he (at least) can perceive sound differences in (different) non-Greek languages. To him, it is clearly not all 'bar, bar...', and he never uses the word onomatopoeically. Instead, for example, he describes one language (that of 'Cave-dwelling Ethiopians') which
resembles no other, for in it they squeak just like bats.
Aristophanes, who rarely missed an opportunity to poke fun at all and sundry, also does not use 'bar, bar, bar...'. Instead, in the Birds,
The speech of these barbarians is quite extraordinary: when they speak Greek, they use poor, broken Greek, and when they do not, they use a very bizarre, nearly indecipherable mix of gibberish and non-Greek languages.
Source: C. Bravo, 'Chirping Like the Swallows: Aristophanes' Portrayals of the Barbarian "Other"'
Aristophanes also refers to
chirping like a swallow, i.e. spitting out nonsensical gibberish.
Among academic works supporting, albeit sometimes tentatively, a Sumerian origin (via the Asiatic Greeks) are: