"My process is to rough-cut the main audio into three segments to correspond with the video clips. Then put two videos and the corresponding audio into a folder and sync the clips"
Not quite sure what's happening here. You have six clips, three for each camera I gather, and three audio clips. Are you building all these nine components into a single sync container? Maybe you could double click the sync clip to show what's inside it? You perhaps can build the entire project inside the clip container.
What I think I'd do is take the video from one camera, the long shot, and sync it with the audio. Then do the same for second camera. Put the two sync clips in a project, stacked on top of each other, resized and repositioned, then cut out the segments in the show you want to delete in the project timeline. It's really simple, select the clips and use Shift-Cmd-B where you want to cut them both.