Do stage text always have to be layered on the top?

If you are willing to have it be on top only during editing, you could use bitmap caching techniques to allow its rendered version to live within the display list, like the NativeText solution documented and provided here:

Native Text Input with StageText

According to Stage Text documentation :

StageText - Adobe ActionScript® 3 (AS3 ) API Reference

When native inputs are used, StageText objects are not display objects and you cannot add them to the Flash display list. Instead, you display a StageText object by attaching it directly to a stage using the stage property. The StageText instance attached to a stage is displayed on top of any Flash display objects. You control the size and position of the rendering area with the viewPort property. There is no way to control depth ordering of different StageText objects. Overlapping two instances is not recommended.

So, according to current implementation, it will not be possible to overlay other Flash Display Objects over Stage text. Will update you if I come to know about some way or workaround.