On the issue of whether the mission was abortable or not, I'd solidly say not. After all, Kirk seemed to sail into the storm with the sole purpose of sailing into the storm! This was a ship-jeopardizing act that caused significant material damage even when the mission was a seeming success (notwithstanding the faked death of a crew member), and might have well cost 430 lives, yet apparently Starfleet wanted Kirk to do exactly this.
Kirk went into the storm, with his seat console specially configured so that he could jettison the pod. It seems clear that his intent was to jettison the pod, sooner or later. At no point in the dialogue did the possibility arise that the pod might not
be jettisoned; all parties seemed aware that it eventually would be, because no verbal commands or comments were needed when the jettison in fact took place.
"Pod", "probe", "bell", "sonde", "rover", "buoy"... All sound like acceptable names for a measuring station to be immersed in a hostile environment. And every other pod ever mentioned in Star Trek has been a free-flyer. (Or a jettisonable, like antimatter pods.)
If Finney's death was needless and fully preventable, then Kirk should've been facing an investigation & court martial as soon as he arrived at Starbase.
Yet Kirk doesn't face investigations and court martials whenever he returns to starbases after losing a Security redshirt on landing party duty. Needless deaths are no doubt routine enough in the Starfleet line of work - and I dispute the idea that Finney's death at pod jettison (say, him being still aboard the pod, or in such a location that the launch would kill him) would have been preventable. Kirk never checks that the shuttlebay is empty before ordering hangar doors opened. Apparently, he relies on his trained crew hearing the klaxons and seeing the signal lights. And those are the very things activated by pressing the alert buttons...
If Finney died despite being informed of the situation, it was his own damn fault. Kirk's task wouldn't be to hold the hands of his crew - it would be to correctly signal them so that they can do their trained jobs.
Instead he doesn't get into trouble at all until the Commodore suddenly realizes the ships records don't show they were yet in a Red Alert situation, and it's that specific focus point that suddenly shifts the direction of the entire episode.
Which negates the idea that losing a crewman would be punishable in itself.
Kirk's crime is "wilful perjury", or lying about the details of the death. It doesn't matter what part he lied about, the crime is that he lied in his detailed report and maintains the lie against Stone's verbal inquest - and thus in all probability is trying to hide other, worse crimes. The exact timing of red alert is not his crime, it's merely the thing he lied about, the hint that he has been up to no good.
Of course the court homes in on the red alert issue: it's the only fact at their disposal. But prosecution isn't really concerned about that. Prosecution's attack is directed at Kirk's person from the very start, with the intent of establishing hostility between him and Finney - and the red alert records are only brought up once it has been concluded that Kirk might have had a motive to murder Finney, and are shoehorned into the scenario where such a murder did take place.