Mineral oil is a lot thinner than castor oil if I recall, might help it move a little better without pushing it through. Hopefully the sharp end got worn down while it was in the gizzard.
Wishing you good luck!
Here's one of my hen's x-rays that shows a screw, and a staple or two. Although this was in the gizzard at the time I have no idea if it passed. The very same week I was talking to my neighbor who explained how his little hen started picking up screws right in front of him while he was at his...