That's certainly what I'd do - go down to the bare trunk, and regrow the branches that I wanted in the places and shapes that I wanted them. With an olive, that shouldn't be too terribly hard to do. I wouldn't advise one to try it with a hinoki.
Looking at your mother-daughter virtual again, Al, I like it a bit more than I did last night. If the branch just came off a bit lower - across from the bulk of the bulging base of the trunk - it would have a wonderful Chinerse flair to it...
...but it doesn't, so I'd remove it. I don't find jin to be particularly compelling on olive unless integrated with very detailed deadwood carving on the trunk itself. So I'd recommend against creating a jin out of either branch.
-OMC