I have never done the above but that might help speed up what I do.
First, break the record thumb of the cameramen, then
Make a sequence that TC starts at the same spot as the first clip, then place all the clip at their respective spots on the timeline, that way the clips TC always matches the sequence TC. This will produce black video gaps where the cameramen stopped rolling.
Finally export the sequence and now you have a single clip of the camera angle that has the correct TC as all the other clips.
Add this to the other camera angles.