I did set up port forwarding on my router for the port I wanted to use.  But yeah, I noticed that my external IP changed.  My 192.168.x.x IP address is static now, but the external one is still dynamic.  

The server doesn't stop on my machine, it stops on machines it's downloaded to.  And Heroku has to give it the SIGKILL signal after a while because it won't bind to any ports.