Get yourself some of those cheap blue rubber or white disposable gloves from an auto parts store. Put one on your "other" hand. (the one not holding the AB).
Spread your fingers inside of the turret race hole, and airbrush without fear of getting paint on your hands. With some careful rotating and shifting-of-fingers, you can get the whole piece painted.
Alternately, make a cheap jig like car modelers use--you can twist a wire clothes hanger into some suitable position and run one end of it through, say, the sprocket attachment hole, or some similar hole.
You can also mount, for instance, a gun carriage or similar piece on a larger piece of sprue, perhaps even an old sprue piece that you cut apart. Use gap-filling super glue to attach the sprue end to an innocuous place on the bottom of the gun carriage or whatever piece you've got. You can always just snap it off later; the attachment point won't be visible. I use this method a lot for small pieces; I have a small box that I keep 3-4" lengths of cut sprue in, and attach parts to them for painting, then recycle them.
These are just some of the methods I use.