What is the most effective way to destroy cockroach and centipede size pests?
Diatomaceous earth (DE) allegedly works very good on most bugs that have an exoskeleton similar to that of an ant or cockroach.  It cuts through their shell, exposing their gooey insides to the air.  Once exposed, they quickly dehydrate and die.

Diatomaceous earth for pool filters is somewhat poisonous, so you'll be looking for food-grade DE or some other form that is nonpoisonous.