Captain Jack would have 6 squares and 1 cylinder, according to the Imperial Handbook.
Here's what I can estimate: Jack Morson (Richard) is the Captain. Corel Kosigan (Rakaydos) would be the executive officer. Kelly (TheTeaMustFlow) would probably be Lieutenant or Sergeant Major. Kael's character hacks it as the chief medical officer; Major doesn't seem to be a rank in the Imperial Navy, as far as I can find. I don't know where Sarone's or Herf Nerder's characters fit in yet.
I'm thinking of using TTMF's suggestion, with the Kuma be suffering from a low crew and possible some battle damage. If we apply the rules for reduced crews (SoR p. 60), the Kuma can be running on a light crew, or a little over half it's complement (about 460-70 crew). That puts some pressure and stress on the crew, especially if they get put through some tough circumstances. That would also cut down on the troop complement, from 75 to about 30-40 (roughly 3-4 squads of stormtroopers). Starfighters I'm not sure on yet, depending on how Herf Nerder develops their character.
TTMF's other suggestions are pretty good, especially of Jack is the newly promoted captain and the previous captain is unliked and responsible for whatever it was the ship just went through. So take a recently weakened and stressed crew, support them with a small number of conscripts and such, make them all operate above the standard, and then shuck them off to unpleasant parts of space. Toss in a few crimes against sapient life and you have to wonder if they weren't trying to get the ship to defect.