I would try a microfiber cloth and some stropping compound (normally used in knife sharpening). Put a few drops (or a dab) on the cloth and rub them on the scratches. I'm guessing this will take them right out. Not sure how many microns on the compound but I'd probably start with 4 micron and see how that works. You may need something more or less coarse. I'm just thinking out loud here.
Being a Cubs fan, you'll appreciate that you get to Strop your scratches right out!
=R=
Same planet, different world