Another great episode! I am very excited to see how your game turns out and FWIW I think you are approaching it exactly right.
Saving the game state on the server is the way to go. You can ensure that state is synchronized on both clients this way by ensuring no moves are registered client side until the server has been successfully updated. You will be able to use error handling/retry logic to ensure communication problems don't cause the clients to become out of synch.
Once I find some time I would also like to take a crack at a multiplayer game for the C64 w/Flyer. Sounds like a lot of fun.