Brandi was sort almost the same way except it was with kitty poo. I would just chase her all over the house trying to get it out of mouth. Finally I had to get a lid for the cat litter and position in a way that only the cat could get to it. Otherwise I am sure Brandi would have kitty treats all over the house.
I know it doesn't help in your situation but doesn't it feel a little better knowing your little girl isn't the only one?

By the way, Brandi has also eaten the cat's furball (vomit with cat hair in it) as well as her own vomit

I watched her vomit, by the time I came back with something to clean it up, she was licking it up! I couldn't believe it. How's that for nasty?