Something else just occurred to me...
If it would be possible to recover these noise and distortion products, could
they themselves be polarity reversed, and recombined with the first dithered 16 bit bouce? In theory, doing this would remove (cancel) the noise and harmonic distortion generated by the process, but the benefit of the dither would be retained (because the file is already 16 bit, and was bounced with dither applied). This combination could be re-bounced, and kept at 16 bit resolution.
I'm absolutely sure there has to be a flaw in this thinking somewhere.
Ben B