This is an interesting question, and I don't have anything especially technical to add that would be helpful.
However, I did recently attend a conference talk by Christopher Ehret of UCLA (
https://en.wikipedia.org/wiki/Christopher_Ehret) who has been working on the sub-groupings within the Afro-Asiatic family. The resulting grouping is roughly as follows:
Omotic vs [Cushitic vs [[[Chadic vs. Berber] vs. Egyptian] vs. Semitic]]
[TREE][Afro-Asiatic Omotic [| Cushitic [| [| [| [Chadic] [Berber]] Egyptian] Semitic]]][/TREE]
In other words, tracing the history of the triliteral root system (a question I asked him after the talk) would mean explaining how it settled in for the ancestor of Semitic/etc., and then faded out from Egyptian to Berber to Chadic. (There still are some remnants of it in Chadic, but it's not nearly as central a feature there as in the others.) And that overall seems to make some sense. So Egyptian is then somewhere between early Semitic and early Berber use of the triliteral root system. (The writing of course, and due to contact, sort of predates the others, in a different sense.) Maybe that would be somewhat helpful to you.
Your question is an interesting one and I wish I had more help to offer.
Another source to consider, of course, would be place names (toponyms), if you could accurately figure out how they were originally pronounced, and also which roots they relate to. But the problem with anything like that, and this question in general, is that there are just three major vowel contrasts, and they can shift a lot, even within the same root based on the root-and-pattern morphology.