What about some mineral oil? or maybe like a smaller Q tip and some KY jelly or something to maybe slick it up and help it pass thru? If she's bleeding, I think you might be best breaking the end of the egg at that point and letting it collapse and help it out? I can't see where that would hurt her much more than she already is. Oh man I feel so bad for her.
This sounds gross but, if you can break a small hole in the end of the egg that's visible, maybe carefully with a drill bit or something, and get a pinky finger inside the egg, inside the hen and like hook your finger over a bit to kind of grab the egg from inside the shell with your finger and gently give a bit of a pull to assist in the process of trying to move it through? Another insane sounding idea and youd need help with it, get like a very small suction cup dart, put a dab of crazy glue or adhesive on it, plop it on the egg and gently pull, help pull the egg out. worse case you pull a plug out of the egg but the device is out of her.
If there was somehow to adhere to the egg w/o having to get a finger or something in there around it from the backside, which would of course further stretch and harm her.
Aaron