My question is: does a task order PoP need to conform with a BPA PoP, if not explicitly stated in the BPA?
The ACO's statement that the period of performance for both the BPA and task order "need to match" is arbitrary and contrary to the language in the BPA itself. The fact that your legal counsel supports your position is further confirmation. If you indicated that the contractor objects to having to perform the task order in this circumstance, it could complicate the situation. However, this doesn't appear to be an issue. At this point the disagreement requires management resolution, as it appears the ACO cannot provide substantiation for his/her statement. You should arrange a meeting or teleconference with both the ACO's supervisor and your supervisor in order to move forward with the task order.