It really seems to me as if the DVD Audio Extractor step from the MakeMKV files is where the click is introduced.
That's my guess as well. Does DVDAE have the option to extract to a single long file?
Is there another app for Mac that maybe could just rip the audio from the MKV files as one long track with no breaks? I could then take what I need as one long 5.1 file and save it as a FLAC.
SoX might be able to help, but it's a command line tool, so it might also just result in frustration.