[Arran]

I would get some of the old fashioned pain and varnish remover and apply that to the stubborn areas, KleenStrip is one such brand. Then I would wash the cabinet down with acetone or lacquer thinner to get rid of any residue. Don't worry about saving the original Philco decal, Radio Daze has proper reproductions now so the old one is just going to get in the way of refinishing. If those black marks are stains then the only way to get them out may be to use bleach, if they are iron stains phosphoric acid will also remove them.
Regards
Arran