Hello,
as you probably already know without opening a port, normal master-master or master-slave replications are impossible. The changing IP is not an issue as long as the MySQL user is not restricted to particular one.
If periodic sync is not an issue for you, then I can write a program to do this for you, but I need to know is the remote server running Linux, and do you have SSH access to it if so? If you don't have SSH access then the solution will become a little bit more complex and my bid would be different.
Kind Regards,
Stanimir Stoyanov