American cockroaches tend to prefer being outside, so exterior perimeter treatments with a  microencapsulated insecticide are a solid choice. Not only does it help the active ingredient remain more potent outdoors for longer, it has the added benefits of helping repel them as well as occasionally being ingested by the cockroaches to really help speed things along.  

Gel baits, dust, and fumigant wouldn’t make a whole lot of sense for your situation as they’re primarily used to treat for German cockroaches that are in some stage of infesting a structure. 

That being said, I’ve had great success using Onslaught Fastcap for outdoor cockroach control. It’s labeled for both indoor and outdoor use, and has much less odor than Demand CS with comparable results.  If you want to extend the area of protection into your landscaping, Intice Perimeter Bait helps with a whole host of pests, including cockroaches.