crickets do not bite people, I don't know where you guys are getting that from

You're probably feeling their legs trying to dig or escape, their mouths are not big enough to bite us.
To the OP, it sounds like your solution would be to cup feed. provided that your cup is steep enough, you can put feeders, including crickets, in there overnight. That way they can't escape and bite your cham.Another option would be to get smaller crickets, that do not bite, and let them free roam like you want.