As a matter of fact, I have those parts sitting in my shop that I started working on today. The first pic you posted, I hand sanded it, reason
I was trying to make up some lost time, and I took it to work with me. I sanded with 80 up to 600, then I used a 8" sisal with black emory and smoothed it way out, it was already smooth with the paper but shining with the emory. Then I hit it with the 8" spiral with black, I usually jump to the white with a loose cotton after that, but occasionally I use the tripoli brown. This part did not need anything else but that, oh and the bobs down in the tight spots. As for the large cover, that is a different story, it was a part that had been polished I guess in the factory, but showed some distress from age. It had many pits and nicks in it, which were pretty much in the wide flatter areas. This had to be sanded, I started with 36grit (Yikes!) and worked my way up, it was a tedious part considering I pretty much sanded the whole face down smooth, but besides the more drastic sanding method, it was the same compounds and wheels.
I have all the greaseless compounds, but hardly ever use them. Maybe I use them incorrectly and that is the reason for it. I load my wheel let it dry, but it only lasts for 2 minutes or so. I really haven't played with it much, but I can see that if it was lasting longer, then it is a good product. I have too many things to get done, hardly any time to experiment.
Another bit of info, but also a question for all. I use pretty much black and white on aluminum and stainless, and get good results. I ordered the green stainless, received it today, used it and set it aside. Seems like the compound is greasy on the part, never seems to get a "dry" cutting action, more of a rub up and down the part action. Again, maybe I am not using it correctly, but the white sure works good and the piece looks like a mirror. The stainless I am polishing is Harley brake rotors, so it is a harder stainless than trim work. Any ideas on the green? or personal experience with the stuff and comparing it to the way I did it?