Castor oil is a better choice than petroleum jelly. Petroleum jelly is not a food, and is not intended to be ingested. It's filled with all sorts of nasty stuff. It comes from petroleum after all!

I feed my dog raw chicken, bones and all, and he's fine, but raw bones are pliable. He's a very good scavenger from his street days, and he's always getting a hold of discarded (cooked) chicken bones on our walks. No way he'll drop them, either, once he's got them. So far so good. But he hasn't, to my knowledge, taken on an entire carcass, although if given the opportunity I'm sure he wouldn't pass it up.

Best wishes to a quick resolution of the situation, preferably outside in some wooded area where you don't have to pick it up!