I've been hand sanding a bunch of razors, and I can't seem to get the low grit scratches out. The progression I'm working with is 120, 220, 400, 600 - the only grits I can find in the hardware stores in my area. When I go from 120 to 220, I keep on going until the scratches seem to go away, but when I go up to the next level, it's almost as if I'm revealing the scratches from the first level.

Is there a solution for this? I have been going in perpendicular directions on each grit, hoping it will remove the scratches faster and be more obvious when I make progress. I know I'll need to get 1K or higher to get rid of the 600 grit scratches, so I'm not worried about that for now. I need to make a trip to an Autozone...