[Mr T]

Huumm, interesting question...
If you don't have too many cuts to follow and a program that's not too long, I would roughly locate the cut points, place an audio region on every one of them(could be anything, even silence recording->this wil just be used as a "location display") or a marker (I think the "audio region trick" is faster though...).
Then I would put the edit window in wide zoom mode (thus giving you access to a frame by frame video window display).Now, clic on the track you've placed audio regions on, and go to the first audio region by using the Tab to transient arrow. Clic on the region; now that you are in wide zoom mode, you should notice that the region is not really on the precise video cut point; just nudge the region so that it's placed on that precise point. You're done. Go to the next region (still using Tab to transient), and so on...
I have to admit I'm giving you this advice based on different other edits I had to perform (SFX, foleys...), since I never had to write music precisely following a video editing (cut points) as it seems to be your case. My experience is that if a client wants the music to follow the video, the music is always made first and it's the videoediting that will have to follow (wayyy easier).
Hope that helps and doesn't confuse...