How are her long hang pullovers? Like in the level 5 routine? And how about baby giants? Could they try a baby giant from handstand? Or even just a long hang pullover from handstand?
If she thinks she's gonna peel, she will probably try to pull the bar because she thinks that helps her grip it harder. But that actually causes the peeling. Some gymnasts don't like the fall from handstand to hang, and they think they are gonna peel and fall. They try to re-grip the bar when they start the fall. That's why I usually ask beginner gymnasts to open their hands (ie release their fingers from the bar) when starting to fall from the handstand. That way they can't pull the bar at that point and they will naturally have good grip when they close their fingers. I know many coaches don't teach that, but I have had great success teaching it like that.
Also, it's very important to actually hang in the bottom - shoulders relaxed, head neutral, shoulder angle open.