Sorry this isn't the direction the way you wanted to go, but if you want a real improvement on ice on paved roads you need to get real snow tires and I'd have them studded. I run studded tires in the winter and switch out to all seasons the rest of the year. That said I drive regularly on snowy roads all winter. If your situation would just be a very occasional thing then this probably isn't a good way to go. Maybe some unstudded real winter/snow tires.
