I've approached more rural lords than priests, but I might be fishing the wrong hole. Thanks for the advice.
Priests can travel quicker and do not need to pay for troops to avoid risking bandits (which isn't as big as an advantage as before, but can still be useful). Which means they can stay out of their realm and purchase food indefinately, because being out of one's realm means gold comes in as bonds, which is the new and only currency for food nowadays.