I've got to say that Moxie is currently my favorite ability on the table. I think since we're aiming for CAP4 to have more checks than counters, this adds a whole new layer to the risk/reward situation. Taking the chance that you can beat their counter (outspeeding/surviving their attack) means that you've now successfully murdered their counter with your increased attack stat. I think this really fits with the concept well if we're hoping for CAP4 to take offensive risks. When using CAP4, you're going to want to risk KOing something in order to get the boost and cause further mayhem. I like it a lot.
Other abilities I like are Illusion and Magic Bounce. The former is really interesting because there honestly aren't that many Pokemon that CAP4 can pose as that are frequent in Overused. It's weak to both forms of hazards. However, it invites the situation that your opponent might not use both forms of hazards, so you can take the risk to use Illusion on CAP4 and hope for no hazards and/or keep them off the field. Magic Bounce is cool for the reasons listed, but I fear that it may become overpowering, a la Krilowatt. I'd need to hear a good case for it, and I think it has potential.