Removing corrosion from cast aluminum

 I have done what you are doing long ago.  My original wheels were beat up from the previous owner even though the car only had 60k on it when it was purchased because the lady didn't know how to park.  It had curb rash and paint that had abrasions mixed in with some corrosion.   

The earlier 2000 wheels is fully painted where the 2003 wheels are half painted and on the face there is some kind of clear coating that shows off the polished aluminum. This clear coating is what stops aluminum corrosion.    

 I tried to make my 2000 wheels look like the face lift by taping all of the wheel arches and exposing the face. I then used aircraft paint striper which worked well by bubbling up the paint but there were some suborn areas that needed to be scrubbed off.  I then machined polished them up with some Mothers Mag polish and the result was good but there was sill pitting and some staining of the aluminum that I could not get out so it wasn't worth it because it was too deep that if I were to be aggressive with it then the wheel finish would look wavy.  

 Eventually in time the exposed aluminum corroded. I would polish them back every 3 months but the staining and pitting got worse.  I eventually sold them to a MK1 guy after buying a good set of wheels.  The end. 

I did some research and there were some products that claimed that they seal the pores  of polished aluminum wheels so they resist corrosion and there might be other options of clear coat for wheels that you should look into but if you do nothing it will get worse.  

If you want to preserve them your best option is paint.  

@dev

Thanks. I will add all this to my project post. The wheels I have are all post-facelift. Two are in great shape (thanks again, pwnzor). Two are rough, and just like yours, the P-PO (PO could drive, not sure about the first owner, tho) curbed them mercilessly. I wish the curb rash were the worst of it, I can mill that away.

I bought a special miracle sealer, maybe one of the ones you looked at, but again I will save that for my project post. Right now, I have to get down to bare metal to apply it.

I've already put about 80% as much effort into it as I am willing. The bar is low - these are just intended to be my salt-soaker winter wheels, but if soaking in vinegar, lemon juice, or unicorn essence is low enough effort, then I can give up a little more elbow grease.

I haven't ruled out painting them eventually, but it is not my first choice.

Mechanical removal of corrosion on aluminum is the best way . I don’t know of any chemicals that will eat the corrosion without eating at the aluminum. Sanding would be your solution. Start out with 220 and work your way up to 3000 then polish. If you have a steady hand a two inch rotating discs will speed up the process. Not for the faint of heart. I’m sure there is a YouTube video of the process.

Sometimes you just need to take a break and look at someone else's trials and tribulation. Help put things back in perspective. Check out this video of a fellow Spyder owner and what he did at around 6 hours per wheel. You only have two - ha!

I have to say, those do look good.  Even on the junk pair the milled faces on these wheels are all in pretty nice shape, so I will be going a little out of the way not to disturb those surfaces.  I'm still not sure I want to do all that sanding (I worked in high-end cabinetmaker shop in college, and I can rock some detail sanding, but then again, UGH).  However, I could use a machine everywhere except the sides of the spokes and just do that by hand.  Wire on the inside of the barrels might be sufficient. I'm working with acid removal of the corrosion over on my how not to restore wheels thread. Perhaps some hybrid approach is in order.

The thing is, if my shortcut rush job only gets me through this one winter, I can always use abrasives later when the schedule is more forgiving. It's the same amount of work as if I do it now, I just waste a bit of expensive protectant finish that I will be sanding off if that's how it works out.

Mechanical removal is generally the only way as CSPIDY point it out but if you do it wrong you will have high and low spots and it will make the finish on the wheels look off with distortions and wavy patterns.  It will be an eye sore to look.   I would try to do this with the least aggressive method with machine buffing and don't sweat the blemishes too much.  

Perhaps if you use plastic media blast to the sides of the spokes to removed the corrosion. Then use a filler, sand and paint the sides. Makes a nice contrast with the polished surface. I did mine in black. You could even match the body color.

if you use sand or glass beads you will distort the surface and have to sand to get smooth.