One more alternative would be to sand the tub evenly dull with
2000-grit wet paper, and then restore the shine with increasingly finer
buffing compounds. This is something that is within the capabilities
of the average DIYer with enough elbow grease. I've taken scratches
out of my Jacuzzi this way.

Oh, by the way, never ever scour your tub with the green side of a
Scotch Bright kitchen sponge.