Hmmm. I wonder if it would be possible to trade your green tin for someone's solid black tin. Then if you still really want satin black, you might be able to lightly sand the clear coat, being VERY careful not to break through to the base coat. I wonder if that would get you the matte black finish you're looking for. Or, you could sand down the black and have it re-clear coated professionally with a satin finish clear for an affordable price.
Dunno. Just kicking out ideas. I'll ask my painter if sanding a clear coat to get a satin finish is a good idea or not. I didn't sand mine down when I had it painted a few years ago, I had it professionally stipped bare. So I have no idea how thick the factory clear is.