Schwinn chrome holds up well when using S O S pads.
I no touchy any chrome wit steel. Not in 0000, not SOS, nope, bad, bad, bad. Brass and aluminum foil good, but steel blows.
SOS soap no helpy either, bad, bad, bad, worse than 0000.
If brass brush or Alum no workey then get Oleic acid bath. After all, most rust is more fungal than penetrated and spoiled, seeped out of microscopic hole in chrome and then coating the chrome surface. once you get that top coat layer off, at least in decent chrome that has a nickel or copper sealer under the it, they be plenty shiny to see. [wink]
With that said, there is occasion for 0000, in my tool book. if somebody etched the chrome already wit SOS or 000, 00 or steel, or stainless brushes then you may buff the deeper etches down if ya got the elbows for it. 0000 scratches mo better than 000 or 00 ones.