I've tried similar ideas with a few pieces of equipment and it's been my experience that, while it may work well in a particular situation, the effort and risk involved haven't usually been worth it for me.
I wouldn't try the rubbing compound or scratch remover option unless you can remove the faceplace and all the knobs so that you can treat the whole front surface identically. Applying either to just the area of the scratch will almost inevitably make the area around the scratch look slightly different from the rest of the surface even if it does hide the scratch.
The whole surface will have become oxidized over time and polishing any part of it will return just that part to something like the original finish. It's very likely that you'll end up with something that looks worse than the scratches you've got now. If there is any lettering on surface you run the risk of affecting it, as well.