The super-glue is a great idea. I haven't tried it, but I think I see where it could rejunenate the part as well as extend it's life.
First clean the part thoroughly. I think Goo Gone would work very well. However it leaves a lot of residue, so once you're done with that clean again with rubbing alcohol. Make sure their is no grease or residue AT ALL.
Now comes the super-glue. As I said, I haven't done this, but do use it on all edges after sanding to eliminate delaminating. I think the same basic concept applies here.
Once the part is cleaned and dried, lay it horizontal and fill the gouges with super-glue. Don't use more than you need, then allow to settle in and dry. If you still notice troughs after drying you can add more. Try avoiding creating any hi spots to avoid having to sand.
Now the final step is polishing. You may be able to use a good quality chrome polish, but I'm not sure. Definately use a soft cloth to apply, and maybe a good quality automotive finishing polish would be better. Test a scrap piece or a spot that isn't visible and see how it comes out.
Once you're done I suspect that you're going to have a part that looks good as new and is more resistant to further scratching.