The critical issue in Fax over IP with a fax machine is the analog to digital conversion. Many ATAs do a very poor job at that, either because they overdeviate the audio or they introduce other types of distortion. My experience with Cisco ATAs is that they do a poor job at accurately reproducing the audio.
Get rid of the Cisco ATAs and replace them with an Obi 200. I use them all the time for Fax Over IP using G711 with ZERO problems.