I am not sure about leaving it as a jin, shortening it, or just removing it....
I picked this tree up at a club auction for just a couple bucks.
I wonder why everyone else passed it up?
Privet Ligustrum x vicaryii shown right after purchase, about 2 feet in height.
They passed it up because it sucks. I can't believe someone with your credentials would buy such a thing. You better not tell anyone else or your reputation may be at stake.
I would remove it. To my eye, it is too far from the nebari to really work as a second trunk. Even if you were to shorten it to a stub it would look like a piece of misplaced deadwood rather than a jin coming from the base of the tree. I would take it out and focus on the single trunk and getting the branches perfectly arrayed to reinforce the lines of the design. That is going to be your challenge - privets throw out a lot of growth so it will be tough to keep a tight design, especially on a smaller tree.