What about dance shoes or theater shoes? Character shoes usually have a little heel, but a strap.

My DD cannot wear flats that do not have a strap or a loafer style. We have had some luck with flat character shoes.

Also, if her feet have stopped growing, it might be worth investing in a "dressy" shoe. She will wear it again...

Good luck!

I just saw your update; what about a simply ballet slipper or "jazz" slipper? If I remember correctly, the jazz slipper has a little heel (like 1/4")