If you want to interpret that way then you need to be able to prove that launching the pod was part of the mission.
Not really. I only need to claim it. Everything else follows from the claim.
The problem is that the claim meets none of the criteria set forth by the episode. I doubt the mission was to launch the pod. If it was the dialogue would've at least mentioned prepping it for launch. Instead we have from the dialogue:
That there is a list of crewmen that take turns to go into the ion pod:
KIRK: Weather scan indicated an ion storm dead ahead. I sent Finney into the pod.
STONE: Why Finney?
KIRK: His name was at the top of the duty roster.
STONE: If he blamed you
KIRK: He may have blamed me that he never rose to command a ship, but I don't assign jobs on the basis of who blames me. It was Finney's turn, and I assigned him. He had just checked in with me from the pod when we hit the leading edge of the storm.
And inside the pod they take readings
FINNEY [OC]: Finney here, Captain. Ion readings in progress.
And the ion pod must be jettisoned in an emergency:
KIRK: Given the same circumstances I would do the same thing without hesitation, because the steps I took in the order I took them were absolutely necessary if I were to save my ship. And nothing is more important than my ship.
KIRK: I agree. I waited until the last possible moment. We were on Red Alert. The storm got worse. I had to jettison the pod.
But the proof is obvious: a dedicated button was installed* in Kirk's very command chair for launching the pod. The jettison was not just part of the mission, it was the mission.
Are you also claiming "Yellow Alert" and "Red Alert" was also the mission? It's pretty obvious that the jettison button there is because only the Captain has the authority to eject the pod. Plus if the emergency created by the pod in a force 7 ion storm was that great, it would make sense to cut out the middle guy when hitting the eject button. That also conveniently makes Kirk on the hook if something went wrong - thus the episode