I've seen a hornet dive bomb a katydid so hard it split it in half then flew off the the upper body. Hornets are great beneficials in spring- early summer while they eat meat but in fall they eat a lot of my fruit and will sting you while picking fruit so they become more of a pest later in the year. A Praying mantis will eat anything including birds, frogs, bees, and other odd things you wouldn't think they would. They are the sharks of the insect world and will even bite you.
Chillybean native or not there is no way I'd relocate stinkbug eggs. They are a huge problem in agriculture because they have so few predators and have a wide range of host plants. The spray from stink bugs have also been known to cause respiratory issues for some people and can cause a bad skin rash. They are good for absolutely nothing in my eyes.
