My scenario, one out of the several possible:
1) Ion storms are rare things (Kirk met three in TOS) that warrant study even at the risk of losing a starship.
2) Studying them involves flying into them and deploying an Ion Pod at a suitable site (the center, the deepest the ship can reach without blowing up, whatever)
3) The pod needs to be primed for its mission just before use; there's no time to do that first and then fly into danger because the rare storm might dissipate in that time
4) This can be done by people who have the extra training, but nobody has this as his or her sole duty aboard because that would be a massive waste of manpower; hence a shortish duty roster, which is at the fingertips of the computer-savvy Records Officer, but not too blatantly so
5) Finney himself is on that roster, and has decided that framing Kirk for his own death in an ion storm is his best plan (he doesn't need a real corpse, he can control the events and the evidence with his special skills, and he automatically eliminates himself from the list of suspects)
6) He now waits for a storm; since there were three in TOS already, perhaps he could afford to skip some during those seven years of waiting, so as to further dissipate suspicion
7) When the perfect storm comes, he has rigged the roster so that he's on top
8) He rushes to the pod and, at a suitable moment, phones Kirk to tell that he's in there, initializing everything as he should (the "ion plate readings" have been turned on already, but further work remains to be done), and then rushes out
9) His software tricks ensure that the CCTV makes no record when he escapes to a hideout he has kept stocked with survival stuff (such as somebody else's gold uniform with the wrong rank braid - he doesn't want one of his own to go suspiciously missing, or perhaps the wants to make his escape as "Full Commander O'Malley") for this opportunity
10) Another trick he triggers corrupts the bridge CCTV to show that Kirk is guilty of at least negligient manslaughter
11) Meanwhile, Kirk reaches the optimal spot for deploying the pod (or decides that his ship is suffering enough as is), and deploys it; it's a tense situation, with Kirk juggling multiple variables, so he makes no further call to Finney, trusting that he had gotten out at the Red Alert signal already
12) Kirk flies the ship out of the storm, sighing with relief
Finney then snickers in his lair, waiting for the chance to jump ship. This may take a while, what with Kirk being kicked out, a new skipper summoned, and the ship performing missions to unsuitable destinations until finally she hits a port where Finney can beam down and disappear.
Timo Saloniemi