I think that would be a nice twist at this point. Back in the day, no one wanted to see her do anything bad, because she was America's Sweetheart. Her handlers, from what I remember reading, helped make sure her earlier breakout roles were of the innocent good girl variety.
If you Google around enough, you'll see where even "Flatliners" was supposedly altered to make her character likable, unlike the other people who actually DID do bad things. Ever notice that? Julia's character simply "misunderstood," and thought she'd wronged someone. She didn't actually do it. At least in the final draft of the film.
At this point, as I've pointed out in a recent thread, she's so famous, she can hardly disappear into a role. Especially, to your point, one in which she's sweet and kind. We've seen her in those for over 25 years.
I think she should take on the role of some sort of psychotic woman who DOES do bad things. She should stretch her acting chops a bit more, and that might be the ticket. No one would buy her being bad in the '90's, but maybe she's to a a point where people want to see her play someone other than herself.