gunnerasch
With castings that are that pitted and corroded you would be best to start with some 120 grit silicon carbide sandpaper, the "wet/dry" black colored stuff.
You can use this paper wet which will wash away a lot of the loose metal particles. Doing this will help prevent the grit from "loading up" with the soft aluminum.
Don't be too quick to change to finer grit papers as any pits left will not be removed by the later sandings while using the finer grit papers.
After removing the pitting by several hours of sanding then start using finer grits like 220. After the 220 switch to the 400 grit.
When the surface has a uniform look from the 400 grit paper, only then should you start thinking about polishing compounds.
Although they make 600-1600 grit wet/dry paper these are really intended for use on paint and you really don't gain much by using them on bare aluminum.
In other words, stopping at 400 grit and going directly to polishing is about the same amount of work as using 1200 grit paper which will still require polishing when you've finished using it.
I forgot to mention that if the surface is flat, use a small piece of wood to back up the paper. If the surfaces are curved just use your hand to back up the paper.
Also, because the final finish will be polished, the direction of sanding should be changed every few strokes. That way, the grit will be sanding off the grooves left by the last few strokes which will result in quicker metal removal.
If you have an electric drill that runs fast you can buy a spindle adapter that will hold a cloth buffing wheel.
These can speed up the process.
If you have access to a bench grinder with a 1/2" axle an even better approach is to buy a 8 inch cloth buffing wheel and mount it on one of the grinders spindles.
There are a number of buffing compounds that can be used with these 8 inch wheels. You apply them to the wheel to "load it".
In the U.S. I've found compounds and wheels made by Dico to work well.
The best compounds for polishing metal is "Stainless" and "Chrome". The Stainless works the fastest and using it will turn your unsightly covers into mirrors.
These can be used with the hand drill buffing wheels but because of the lower speeds of the drill it will take longer than if you used the cloth wheel mounted on a bench grinder.