A lot of good advice on here, some worth trying but I think it's best to leave well enough alone, meaning he's ok alone (with the skirt tetras). There are in fact exceptions to the general schooling rule, I have a neon tetra who is much happier alone because the others attack him (the opposite reason of yours). And like you said at first, he's survived your learning curve so he is definately one of the fittest and why you should keep him! I have the utmost respect for my survivor fish (of my beginner mistakes).
Sounds to me like he's telling the other black Tetras: "I'm the fittest and I'll prove it to you".
So leave him alone
It's normal to be "toughened" when you're a survivor of hard times - so yeah, he's a bully now (and probably why he survived), just see him as your Tough-tetra