I think you're really doing everything you possibly can at this point. As long as you know she's comfortable and not disturbed, and you do your best to stay consistent, I can't see that you're doing anything wrong at all. I wish I had some better advice for you, BUT I strongly feel that she should see a doctor, because that's really not normal and definitely not healthy for her not to get adequate sleep.
Also, take away the nap!! Then she'll be more inclined to get some sleep at night that she isn't getting during the day anymore. She'll at least be more tired. I've found that even just a half an hour during the day can completely destroy my son's night sleep. All kids are different. A lot of kids still nap until their school years!! I did. But my son just isn't that way, and maybe your daughter is the same. Give that a try for a couple weeks and see how it affects her, and take her to a doctor for sure!!