I'm running Ubuntu 18.04 and using kdenlive version 17.12.3.

When I drop a clip into kdenlive, and try to preview it, the audio does not play. The program acts as if it is playing audio, shows that there is audio to play and wrenders with audio, but if I check the applications that are playing audio, kdenlive is not listed. I've tried the solution in this thread https://ubuntuforums.com/showthread.php?t=2275491 which has worked in the past, but now causes this viewtopic.php?t=151217 to happen.

I think you have to activate PulsAudio. Or you download the current Kdenlive AppImage version 18.12.1b
https://files.kde.org/kdenlive/release/