I've done it with great results. There are chemical methods of removing the anodized layer but I used my mouse sander with fine grit sandpaper. After the fine grit on the mouse sander (forgot what I started with) I used I think 3 more finer papers going all the way down to I believe it was 4000 grit. Then I bought the metal polish kit from harbor freight that comes with cotton wheels to attach to my drill and the 3 different compounds (grit) for polishing. If I remember correctly, I only used the 2 finer compounds. Basically you just need to sand finer and finer. By the time I was done with the sandpaper (and before I started the "rubbing compound" or "jewlers compound") I tested a small section of the grill using something like the compound you tried, but the result was that it scratched my grill. In other words, I had already exceeded the polishing that the common rubbing compounds found on the the store shelf could do...and I still had yet to use the polishing kit.
You might also find some articles or youtube videos on the subject. It can be a lot of work but my end result came out great using this process.
