I think its due to axys conventions which are not the same between BJS and glTF.
That said, to “clean” a model in Blender, apply transforms (3DView > Object > Apply), especially rotation here.
In a particular case where you want modify the origin rotation, the only way I found without using addon is to create a primitive (in object mode, not edit) using the Align View option in the Redo Last popup, having previously align your viewport ortho view using face selection. Then merge your model to the primitive.
Maybe unparenting before apply transforms is necessary. About addon I don’t know one, I mentionned that 'cause I suppose someone already code this kind of functionnality.