My enquiry in NASCAS brought a note from Prof. Samir Khalil, that the Bar Hebraeus reference is actually just a copy of the statement in al-Qifti. Dr Khalil published on this in «L’utilisation d’al-Qifṭī par la Chronique arabe d’Ibn al-‘Ibrī († 1286)», in : Samir Khalil Samir (Éd.), Actes du IIe symposium syro-arabicum (Sayyidat al-Bīr, septembre 1998). Études arabes chrétiennes, = Parole de l’Orient 28 (2003) 551-598.
If anyone reading this has a PDF copy of this article, please let me know!