iMovie 10 adds clicking sound when exporting movie with MTS file

I have an MTS file that I need to use in a movie. The audio of the MTS plays fine in VLC media player. The audio also sounds fine when I am editing the video in iMovie. However, when I export my video to file (MP4) I get a weird clicking sound throughout. At first, I thought the audio was too loud and was "clipping", but reducing the volume before exporting did nothing.

The thread below sounds related to my problem (I only have one file though, not two), but I can't get any of the solutions listed to work. Deleting the beginning of the video does nothing. I can detach the audio like someone there suggests, but I can't export the audio to MP3 (or can't figure it out how). The file can't be imported into Audacity (or Garageband) to get an MP3 of the audio either...

iMovie 10.0.1 exports to .mp4 from AVCHD .MTS files but adds popping/clicking in audio. Bug?

I am using iMovie 10. This file was rescued from a corrupted SD card and can't be extracted in a different way. I also can't just refilm the video. This file is large (2 GB) and can't be converted with any free software I can find. Would prefer free solutions, but who knows once I become more desperate....

Please Help! I really need this file to export with clean audio for a Master's project!