With CMx1 you can use a program called 'PBEM helper'. It makes keeping track of you PBEM files so much easier and does everything for you, from loading the file, putting in the correct password and sending the next file to your opponent with the touch of a button. The other thing this program allows you to do is to watch the battle as a movie, just like you have described. I've added the link below. I couldn't imagine playing without it.
PBEM Helper: http://www.nic.fi/~fuerte/pbem.htm