Lee, thats a great list of skippers from Season 2!
I had in mind Stone from the first season and Chandra and Krasnovsky. Ramart was on my list too. So all good catches.
I also had Captain Merickus on my list, and Tracy. Bad captains! The Captains of the ships in The Ultimate Computer were on my list.
Scott, I had considered Jones's ship for this. And then I thought, it was a private ship, so I thought it didn't belong. Spock being in Command of the Galileo I hadn't considered. But he did have a crew and it was a Federation vessel. I'm on the fence on that one. I figured John Gil was dropped off on the planet and didn't go there himself. But I am speculating. He could have flown a scout ship there. Sevrin was a crackhead and typhoid carrier, so I didn't have him on my list.

So here's who we have so far. Quite an impressive list, some misfits as Lee has pointed out, and dedicated sound Captains too. And kinda cool that we get a sense of so many other ships in the Fleet, yet we didn't see most of them! The Astral Queen is never seen, nor is the Antares until the Remastered.
James Kirk (Enterprise)
Christopher Pike (Enterprise)
Ramart (Antares)
Jon Daily (Astral Queen)
Commodore Stone (Unknown, but he used to command something)
Krasnovsky (Unknown)
Chandra (Unknown)
Matt Decker (Constellation)
R.M. Merik (Beagle)
Garrovick (Farragut)
Bob Wesley (Lexington)
Harris (Excalibur)
Ron Tracey (Exeter)