I managed to reduce the reflections a fair bit with the polariser, but I could not eliminate them entirely. In retrospect I think they work fairly well in the shot, so I am not terribly upset that they are there.
I must say that I am impressed by how sharp this one came out, given that I accidentally shot it at 1/13th of a second. I'd originally been shooting in full manual, but I guess I must have accidentally bumped the control over to Aperture Priority, and I didn't notice the crazy long shutter speed when I left it set to f/7.1. I shot this at a focal length of 75mm, and used a circular polariser to reduce the reflections on the window. I adjusted the brightness and contrast a bit in software, rotated it about .3 degrees counter-clockwise and converted it to black and white with a gradient overlay. Finally I created a slightly larger canvas behind the picture so that I could give it the shadow box effect you see here.