Jen may in pain, but it is not your job, nor the job your organization to "fix" her or be her therapy group. If it helps, you probably wouldn't be able to anyway. Personality disorders are incredibly difficult to treat even by trained therapists. You aren't going to have much luck at all getting her to change.
Armchair shrinking aside, just behavior wise, Jen isn't going to change because she doesn't believe she has done anything wrong. She is, and always shall be, the victim.
Let her go. In fact, I don't know why you aren't all encouraging her to go. When I first read the line about you talking to her mentor to give her encouragement, that's what I thought you meant! Encouragement that this group may not be a good match for her! If nothing else, she will probably stop threatening it if you start agreeing with it because her satisfaction is in having everyone just beg her to stay. If you agree with her and she doesn't get that reaction, she probably won't know what to do.
I will say however, that I think it's really disappointing that you gave her this chance to throw this fit in the first place. A group was already preparing a presentation. Why in the world didn't you just let them? Because Jen makes such a fuss. She is basically controlling the group by making people afraid to deal with her. Is that really how you want to be controlled?
Again, let her go. It's nice of you to care, but other than giving her the card of a good psychologist (if you really think she's NPD), there's nothing more you can do to make this situation better. Your responsibility is now to the rest of the group. They deserve attention too.