Is it painted or anodized? if anodized, use oven cleaner as described in the thread, this should remove the black you can't get to, if painted use paint stripper to get at the bits you can't reach, but it is a little harder work to get paint off. (if you are unsure try oven cleaner on a small patch to see what happens, try this first as chances are it is anodized) once black bits are removed polish and don't worry about coating or chroming or corrosion. to keep a really nice shine you can just give it a really quick polish with Brasso ever couple of months (if you can be bothered)
Is it painted or anodized? if anodized, use oven cleaner as described in the thread, this should remove the black you can't get to, if painted use paint stripper to get at the bits you can't reach, but it is a little harder work to get paint off. (if you are unsure try oven cleaner on a small patch to see what happens, try this first as chances are it is anodized) once black bits are removed polish and don't worry about coating or chroming or corrosion. to keep a really nice shine you can just give it a really quick polish with Brasso ever couple of months (if you can be bothered)