Okay. So coming back more directly to the subject: a couple of thoughts.
1. On the "League" concept: investigating and discovering the "truth" about the League and its Patrons could, it occurs to me, function well as an overall meta-narrative / story-arc for such a series (the crew's "golden fleece" as it were -- I think possibly you already have something like this in mind). That way it could build steadily through a series of reveals and twists and turns about what this entity really is and whether it's a Dominion-style threat or not.
2. One potential problem occurs to me about the "lower decks" concept. Senior officers are a handy vantage point on the events of a series because they believably have a hand in most of what the good ship Franchise is doing. It would be harder to have a group of grunts who could offer that same perspective. That does open up storytelling possibilities too, but it might frustrate people to only ever see their small slice of the bigger picture and the temptation to have them employed in an improbable number of roles would be strong (Space: Above and Beyond syndrome).
A valid point, and I have an answer to it!
First, these junior officers are "on the line" as it were, getting briefed about events as they face new situations and of course sharing their own speculations among themselves.
Second, they would interact with more senior officers. For example, somebody might form a mentor/protogee relationship a la Sisko and Dax, Kirk and Garrovick, Chekhov and Kirk, Picard and Ro, etc. Others could have a more adversarial setup, rather like that between Snape and Harry Potter.
Third, they won't stay at the bottom forever. These are very talented, able young people chosen for this assignment because of that. Over a few seasons, they'll be promoted and advanced to increasingly responsible positions.