Carrots are fine as gut-load. I use carrots for all my roaches and crickets, and my mantis collection is still up and well. Myths like that arise when one or two people wrongly correlate the death of one of their mantises to something like carrots. Their mantises may have passed away from all kinds of random things including improper husbandry.
I personally wouldn't leave any crickets in with my mantises. Crickets tend to attack other crickets or even mantises if they get hungry, and mantises are awfully bad at defending themselves (unless they are hungry and want to eat). They can take 7 days without food with a problem. At 10 days they should be pretty hungry but still alright in my opinion, you should check if there are roach vendors around your area. B. Lateralis and Dubia both will not climb plastic so there is no way for them to get to your mantis and bother them, you can safely leave those inside the container (no soil substrate though, they like to hide). Mealworms might work too if your mantis actively hunts them. Crickets in general are just awful, they eat each other even when they are well-fed >.< Or maybe I'm just doing something awfully wrong.
Good luck! You could always swing by and pick a boyfriend up for your girl hehe.