Split Quicktime Clip Collection Into Individual Videos
I ended up just opening each file in QuickTime and exporting each clip manually. It wasn't the optimal solution, but did get the job done. 

For future viewers, showing package contents on the video file did yield a set of individual movie files in MTS format. I defaulted to manually exporting each clip, however, because I wanted the files in MP4 and didn't have access to a video converter app. However, that would have been a viable option as well.