I'm also writing an online version of a board game I like, to play with family and friends. I am about to start the networking part, and I actually intended to implement the deterministic approach, although I didn't know the concept had a name before reading the article. It's nice to read some validation that it is a good design.
I'm curious to know how you achieve not to need a server at all. How do you create the initial connection between clients without a server to negotiate NATs and things like that?