Are you looking to completely remove the black(ish) areas, including the pitting? If so, some heavy sanding is likely needed. I'm assuming some or most of those spots are probably pitted, so to remove the pitting, you'll have to sand/grind down the surrounding steel. If that's the goal, then I'd use a firm block (such as wood) with wet/dry sandpaper (silicon carbide) wrapped around it. Something like 400 grit to start off, which should remove metal pretty quickly. If it's still going slowly, drop down to 220/320 grit, then follow & refine with 400 and up, taking it as high as you prefer, according to desired finish.
Not sure what the 'Super' polishing paste is made of (abrasive-wise), but you might try some Simichrome or Flitz polishing pastes instead. They both use aluminum oxide abrasive, which is much better at cleaning black oxide from steel. If removing the black oxide only is the goal, without otherwise altering or sanding out the pitting, that may be worth a try, first thing. Apply the paste liberally, and scrub with a cloth or maybe even a toothbrush. The pitting will remain, but the black oxide should come off to reveal clean steel underneath. May still not get it all; some of the 'black' areas may be deep pits in the steel (hard for me to tell by the pics).