A quick fix would be to add anti-aliasing just on the Sprite3D instance, with the help of a FragmentFilter. Like this:
object.filter = new FragmentFilter();
object.filter.antiAliasing = 3;
If that's not supported on your platform, you can also play around with the resolution instead:
object.filter.resolution = 2;
I do wonder why the "transparent alpha bounds" trick doesn't work. :-/ Could you maybe post a screenshot plus the texture you're using?