What I have done is after finding the sync points for clips, stack them on the timeline, as if you were NOT going to multiclip them..in this case 3 vid and 6 audio tracks all synced up. (preferably with markers or inpoints showing the sync points)
Then make a multiclip using just video- not audio- and put the multiclip on the timeline, replacing the 3 video tracks with one multiclip, not affecting the 6 audio tracks. Cant remember offhand if I locked the audio tracks during multiclip editing but I dont think so. I think the cuts affect video only and you can edit audio by hand as you wish.
Hope this helps
Paul