Ok, so, today I went to the dollar store and bought 3 tubes of good ol' white tooth paste for 79 cents each. They even came with tooth brushes (good for parts washing)!
I tried several methods of water, no water, damp rag, orbital buffer, no orbital buffer. My results: A minty smelling, clean, but pitted and scratched windshield.

It didn't even remove the tiny microscopic hairline scratches most likely left by ice scrapers.
Oh well, now I'm off to find a glass polishing system.
Thanks for the recommendation though, I wish it would have worked.