Here is what you may have missed:
1) I am a beginner wirh Final Cut and am notmfamiliar with time synching.
2) I may have been unclear, but I am using one audio-only soundtrack, composed with Logic Pro, and then attempting to match it up with four video clips, each recorded separately, each representing different melody lines – the lede and three backup harmonies. I am using a Canon Vixia HF R60, which I dont believe offers a time stamp, but perhaps i am wrong. Each of those video tracks was recorded separately, not simultaneously, so I am not certain your good suggestion of time synching would work in this case anyway since the time stamps would all be different.