I would go with a barrel with a .689 or .688 bore first of all. CP, dye, planet eclipse all do nice barrels. If you stick with a 2 piece it will still fit in your case. Your standard barrel your using will be a .693 bore so a fair bit of over bore for most paints today. The smaller bore will increase your consistency and there for your accuracy.
The biggest effect on accuracy is always gonna be your paint though. I shot 2 types of paint at the weekend. Both were matched to my barrel. One ball shot all over the place one was ball and ball. A barrel can only do so much...