A couple of points.
One is that James T. Kirk has a nephew, who survived the Deneva Disaster. I presuming this Ensign to be his descendant.
"Campy" presumes a specific style and approach. If I created the impression of campiness, I'm honestly baffled by that fact. But such was never my intention.
could be a smaller vessel, but to be honest given the fictional nature of the universe involved, the decision could go either way. Certainly I'm not wedded to either notion.
The "techno-babble shuttle" is a fun name! But I think frankly I've already justified the idea above.
As far as the League, this was discussed in the What Kind of Character
thread. The idea is for an entity quite like the Federation, in no way "evil" or "oppressive" but a clear potential rival--more, one with various member races lots of Federation peoples find disturbing. Examples: A species of carrion eaters, a genuine hive mind, a warrior race that makes the Jem'Hadar look like camp fire girls, another species on par with the Metrons or Excalbians whom some folks virtually (or genuinely) worship, a hyper-individualistic civilization that seems to operate via pure anarchy, another species that are simply physically repulsive to most humanoids, etc.