Hello mco246:
My ideas on your question:
I think if you apply to NS, you still will be available for other provinces. NS is not going to notify other provinces that you have applied, and even if so, whenever a province nominates you, it will be up to you if accept it or not. If NS haven't nominated you and another does and you accept the other one, that's it. It's your decision in EE.
I will do so, apply for NS and if in the meantime other province nominates me, I will decide if accept it or not.
Regards