One of the issues with aluminum is anodizing. Or, perhaps even a layer of oxidization. Which gets you into an all or none with the polishing.

A good way to polish is just successive sandpaper. Depending on the depth of damage, start low, and work up to 600 or 1000 grit. Maybe oil or polishing compound near the end.

It appears as if your Shimano 600 logo is imprinted into the crank. Be careful around it, but there is not the same risk as simple painted on logos.

Overall your scratches don't look that deep, so perhaps there is a better way.