Regarding: "It appears that the Knights are repudiating their vows and forfeiting their claim to be a religious order, in favor of their identity as a medieval military order. "
- The irony is that the Holy See and Vatican City State have the same hybrid arrangement: religious institution - sovereign state. So, it is unlikely that the Vatican or the Holy See will place the Knights and Dames outside of its (Holy See and / or Vatican City State)  control or influence.
- That written, the Knights and Dames pretty much can rewrite their constitutions and go it alone, and / or maintain diplomatic relations with the Vatican. Though the Vatican insists that all diplomats relate to the Holy See -- though all diplomats know that it is the State with which they interact (even states where separation of church and state is not a strong suite know that they do not relate with the religious institution but with the state).