My JCP only eats mice too. I've tried rats half heartedly with no success. Not sure how big your JCP is but mines about 3.5' and 2 large mice per week seem to keep her happily full. Far as I know JCP don't get as big as coastals and stuff. I think they top out around 5-6' for females which even if it stayed a mouser, 3 or 4 large mice should be good.
I've tried thawing the mice with the rats, offering a mouse and then rat after and nothing. I've pretty much given up personally lol.