I think you may be overthinking this a little. I've heard of plenty of people whose nicknames stem from their middle names, so I don't think it would be an issue if you called her
Jules or Etty from time to time. Some people have mulitple nicknames, and they don't always relate to their given name at all. That being said, I think you should be consistent with what you call her most of the time, so it's not confusing.