Not sure how the dowel would work if I understand that a case is stuck in the cylinder. However I agree with JBnTX and would try the kroil, but beware if the other chambers are loaded with live rounds the kroil can seep into them.
^^^ I believe op said it was stuck forward in a fee w/o primer, not stuck out. Wooden dowel recommendation sounds about right. If the wood is too soft and fp sinks in try to find correct caliber spent case that would slip over the dowel?? Good luck with your fix.