I still have enough difficulty swallowing the idea that the pod would endanger the ship in any way. The storm was already tearing the ship apart, and Kirk wanted to get out to stop this from happening. Whatever problems the pod might have caused, surely those would also have ceased to matter if Kirk commanded the ship out of the storm?
It seems more as if the pod somehow prevented
Kirk from leaving the storm. Yet it sure didn't stop the ship from maneuvering, flying at warp, adding one third more thrust and so forth. So the way the pod kept the ship in the dangerous storm was not a physical one - in physical terms, the ship could clearly have departed if Kirk ordered it to, with or without the pod being jettisoned, but the pod prevented Kirk from ordering such a maneuver.
Which is why I think the idea was that jettisoning the pod in the middle of the storm was the purpose of the whole exercise, and worth risking not just Finney's life, but all the 430 lives aboard. It's also strongly suggested that jettisoning the pod was always part of the plan: Kirk says "It has been suggested that I panicked on the bridge and jettisoned the ion pod prematurely", establishing the idea of a non-premature jettisoning.
There would have been a right time for jettisoning the pod, after Finney was done with whatever he was doing. That sounds to me like the pod was supposed to be launched
, to a free-flying mission, even if the terminology sounds unusual. It's also possible the pod was supposed to be discarded after experiments were completed, but in that case there should have been no hurry: the ship was physically free to maneuver even with the pod attached.