I did not try a further reflection of that kind for some reasons:
1- Too clear reflected elements vs no character reflections = weird
2- To make a quality reflection of all the elements, they would need to be too big for the main model. I've seen you've reflected the left column thing. It's not in the same place in horizontal than the original column for obvious reasons. It looks weird to me.
Anyway, nice attempt.
You could rotate the shadow model, so that the shadow system acts as a reflection.
Shadows act as shadows, and you cannot rotate them. My approach was making them fall towards the camera, so from the distance they look like rotated models. But they're just projected on the floor.