I know exactly where you can put them... in MY garden! I had problems with crickets/grasshoppers when we first moved here. The first year we were infested, we had a prairie toad living in our garden. I didn't mow the grass so he seemed happy to wander where it pleased him/her. The next year, I saw the toad but not as much. I think he/she moved on to hoppier pastures or was taken by a hawk (do they eat them?). Last year, we had a HUGE influx of hoppers followed shortly by a huge influx of mantids. I can not believe how big the biggest one I saw was. She was at least 4 inches long!!! I'm pretty sure it was a female anyway from what I read about them. This year... hoppers beware! Between the mantids, toad (hopefully) and my new chickens, they'll be toast.
Oh how fun! Praying mantises are our state insect, and I just love them. I am going to buy an eggcase for the garden soon, if I don't find one like you did.
Great photos, by the way.