I had a similar problem with my Alfa (Oil running out in about 500 miles without any sign of it out the back or on the floor). Turned out the oil filter was leaking when hot, but the oil was dripping on to the exhaust and burning off which I couldn't see or smell from inside the cabin. I don't know what its like on your beemer but is there a chance that the oil is burning off without leaving any obvious residue?
thats one of my guesses, 1 litre every 450 miles is aprox 2.2ml per mile, which is absolutely bugger all in a hot engine bay the size wales to be burnt unnoticed