I would add my speculation. As the Jews moved in the Sinai desert by the Red sea some individual groups my have wondered south if the Red sea and ended by Sharm All shekh and crossed into Arabic peninsula and wondered toward Yemen and Ethiopia.
Your timeline is way off. By the time Hebrew came into existence as a separate language, a great many other Semitic languages were also established, including Phoenician, Arabic, Aramaic, Ugaritic and Syriac.
Written records in Eblaite and Akkadian go back to 2500BCE, long before the emergence of the Hebrew ethnic group in Canaan.
Afroasiatic is the second most-studied language family on earth, and the Semitic branch of it has been studied almost as intensively as the Indo-European family. We have a pretty thorough history of the various Semitic peoples all the way back to the invention of writing.
There's no room for speculation about events that occurred during historical times. ("History" is written. Events that occurred before writing was invented, and must therefore be studied by means other than simply reading more-or-less contemporary accounts of them, are called "prehistoric.")
The migrations that resulted in the Semitic-speaking (and other Afroasiatic-speaking) tribes living where they were, at the point in time when anthropological research first identifies their ancestors, happened many thousands of years before the biblical tales, i.e., in prehistory.
Throughout the first millennium BCE, Yemen was a crossroads of culture and was host to several strong empires, including the Minaeans, Sabaeans, Hadramites and Qatabanians. They were all Arabian people who spoke Old South Arabic.
As for Ethiopia, Semitic languages have been spoken there since at least 2000BCE, again long before the migrations you speak of took place.
When writing was invented around 3000BCE, allowing ancient people to communicate with us directly for the first time, Semitic-speaking people already lived in both northeastern Africa and southwestern Asia. So we have not yet found a way to determine the direction of their migration.