Beards, books and boredom

Beard (n.) Old English "beard," from West Germanic *barthaz (cf. Old Frisian berd, Middle Dutch baert, Old High German bart, German bart), seemingly from PIE *bhardh-a-"beard" (cf. Old Church Slavonic brada, Lithuanian barzda, and perhaps Latin barba "beard").

I have a etymological theory regarding beards that I might use in my dissertation.
The sources say the word 'barbarian' comes from the Greek 'barbaroi', meaning anyone who wasn't Greek (mostly the Persians) and that in turn came from 'bar-bar' which was mimicking the language of the savages.
I propose that instead of coming from 'bar-bar', it stems from the Greek 'barba' meaning beard. The Persians were a very hairy people compared to the Greeks, and I propose that 'barbaroi' actually meant 'the bearded ones'.
Where my theory falls down is that the Ancient Greeks were very keen on beards themselves, so perhaps further research is necessary.