I know there's a thing called crochet thread, and I think it's more smooth than embroidery thread? Maybe that would work too.

Huh, I've never heard of this. The problem here is that the individual strings sort of went their own ways at times, split a bit. So I was hoping that wax would keep them together. Also ended up with an extra end somehow, and I have no idea what happened πŸ˜‚