Sometimes a villain is a force of nature in a story, an antagonist to make things harder for the protagonist. It’s perfectly fine to have someone like Baum’s Wicked Witch of the West or Tolkien’s Sauron. The point of the exercise is to take a character that has a truly serious flaw and practice creating empathy for such a character. Since most people who take my classes have a lot of difficulty giving the protagonist a serious flaw, it’s about working with what you have — a flawed villain.
So, incorporating empathy into your story for Veronique isn’t the point. The point is to develop the skill so you can more confidently give your protagonist a genuine flaw (in preparation, since it can be dialed down) to explore a big character arc.
On losing yourself as you draft, that’s a great approach. The inner editor should be banished when you sit down to draft. And I’m fine with seat-of-the-pants writing, which means it’s not necessary to outline or explore character arcs before drafting. I think the flaw and the character arc need to be explored at some point, which may be the first rewrite.
Big character arcs and serious flaws unlock the full potential of a story. That can set your manuscript apart from most of the work by other people and, ultimately, lead to more engaged readers. It isn’t easy to do because of attachments to protagonists and concerns about their being likable. It also can be painful if you directly mine your own experiences. You can end up with a draft that goes too far for your intended readers and find yourself pulling back in some scenes. But the advantage of serious work on character arcs that take you out of your comfort zone is the option of adding depth and power to your stories.
So, working on empathy for Veronique is not intended to push you toward making her a more rounded character or including any of that work in your novel. After you’ve learned from it, you can erase it from you hard drive. It’s an exercise to learn how to create better character arc for your protagonist.