Another thought.
If you have access to a smallmuzzle loader ball screw you could put that one your rod, slide it in the bbl twist it in the head of the snake and pull it through without trying to push it back out since the bristles are facing the rear of the bbl as it is.
If it dont pull it through it would at least pull the innards from the snake thus making it smaller and looser.
That screw for a ML is designed to pull out lead balls from the muzzel of course.
Let us know what you end up doing to get it out.
