I would like to commend you for your diligence in pursuing a fix from HP!
I have several M475DW (Pro400) printers. The users are all on windows 7 so I rolled back to IE10. Everything was working fine until the november 2014 patches were rolled out we were back to the same issue. I found the offending patch, KB3003057. I have confirmed on several machines if I uninstall this patch, send fax works again.
I'm curoius if your fix is still working? I saw HP released an updated driver/software package in August 2014 that fixes "Minor communication issues" I uninstalled the printer and reinstalled with new driver. This however did not fix the problem until I uninstalled the above patch. To be fair I only tried this on one machine, I want to do a little more testing. I really dont like having to uninstal critical security patches to get the fax printer to work