I had the idea to have him read rape victim impact statements in front of the entire unit to underline the significance of what he was joking about. Do you think that would be helpful?

No, this will be scoffed at behind closed doors. You're not going to convince them to change their disgusting views most likely. What you can do is be openly hostile towards any sort of talk like that and make it clear they will be dressed down for their shit behaviour if it ever comes out again.

Active bystander skills help change environments. If you're in a position of authority, this is your family and you make the rules for what is acceptable and what is not.