Try using household chlorine bleach. Apply it to the copper then warm the copper with a soft flame from a torch. It reacts very quickly although it may be a bit stronger in color than the patina achieved with ammonia chloride. Some lasers can't handle the reflective characteristic of copper based metals while cutting although when done on stainless steel there is sometimes a peel off covering that prevents this problem. Another option might be to have the copper cut with a plasma torch although it's not quite as smooth as a laser cut.
Third option is to hand saw the pierced designs with coping saws.
Another thought is to check out some sign making companies, they often use a router like device for cutouts. This might be your best option yet depending on how fine your cut outs have to be.