Did you set up your Multicam Sequence using this method:
Create a new sequence, and add the clips to that.
Sync them up. Nest that into a second sequence.
Right click that nested clip and select Enable Multicam.
You've done things backwards. First you edit the entire multicam segment, then you pick out the good parts for use.
Seriously? Isn't that a time waster? There are big chunks of this video I have to edit out. Doesn't make any sense to work that way to me. I was hoping that wasn't the answer.
You can always skip over the chunks that don't need editing, but as a general rule you do use the entire clip for multicam editing.