Is it confirmed that each player can only declare a mil and a pol conflict each round? Where? It doesn't make much sense to me.
Regarding the rings, my guess is that changing the ring of a conflict would change the token, which would free the original ring to be chosen on a future conflict, perhaps by the phoenix player who changed it in the first place. This is just a guess and we'll have to wait to see the rulebook or future previews to know for sure, but I think it's a very clear and simple way for that interaction to work. Much simpler than having to remember what ring the conflict was declared on or what ir it was changed to and also strategically more interesting (imo).