I wonder how old the name Wadi Hawran is. If it is ancient, then I wonder whether it might not have some connection to, or actually be, the “inner Haran” that is mentioned in (and gives the name to) the Mandaean text Haran Gawaita. This fragmentary text begins in mid-sentence with “…and Haran Gawaita receiveth him and that city in which there were Nasoraeans”.
Since the Mandaeans are baptizers, if they originated in the Jordan valley and moved East, they would have to stick to a route that provided access to flowing water. The Wadi Haran seems like a good candidate, depending on seasonal considerations, but perhaps that very issue of the presence of water explains why inner Haran “received him” (whoever “him” is in this context).
Following the wadi would have taken them, unless I am mistaken, through Nabataea, and the Nabataean alphabet presumably contributed something to the script that the Mandaeans came to use. The Mandaic script seems, however, to have been artificially created for the purpose of ritual use, keeping the content of their scriptures and religious texts secret, and adding an air of mystique to their magical writings. It might be going too far to suggest that a number of the characters may have been derived from Hebrew/Aramaic, being modified (and if necessary even turned on their side) in order to make ligature possible. But the lack of any clear instance of the Mandaic script itself used for any purpose other than writing religious texts or magic bowls and amulets may support the notion that the script was created precisely for this use alone.
At any rate, Wadi Hawran would provide a conduit for a group in the Jordan valley to lower Iraq, where the Mandaeans are known to have been centered down the centuries. This also would have placed them in proximity to Arabia, where eventually Muhammad would apparently become aware of them and grant them the status of “people of the book”.