That sounds Larry Niven-esque. That's not a problem. I think great distances in Star Trek (and hence the time taken to travel them) have always been a problem for the show. We had Kirk meeting beings from the Andromeda galaxy one week, from beyond some great barrier at the galactic edge, or travelling to find Sha Ka Ree at the galactic core, while still maintaining that a Quadrant is an enormous distance. Then in TNG and DS9 they has us believe the Bree, Tholians, Borg and Dominion still lived on the edges of known space. Then Voyager being "lost" but getting home using Borg transwarp corridors. If it is that easy, surely everyone used them. Such great distances should have taken generations to cross. So, when they showed Archer and his cohorts breaking early Warp speed records, and tried to make the Klingons seem far, far away, it never felt very believable.
The only Niven I have had the pleasure of reading is Niven and Purnelles The Burning City. Although Niven is on my hit list!
Totally agree with the distances and lack thereof of any internal consistency, I would suggest that they used the premise of the Transwarp from the films as a far more efficient and faster warp travel and just ignored continuity issues. I think a new series would necessarily take a large viewership from fans of the recent films, which includes a lot of non ST series fans.
They could still make the Galaxy reasonably traversable without making the story completely InterGalactic, although if I was making it I would go down that route.
My premise also contains:
1. A crew member from a species believed to be completely extinct, probably at the hands of the Borg and adding extra emotional dimension to this crew members story.
2. A non gendered, non humanoid alien, non oxygen breathing alien. Probably a floating gas bag like a small balloon that also had its own environmental suit and quarters (something B5 did that I was disappointed ST never did.)
3. Wouldn't it be nice to have a humanoid but non human captain, keep them relatively human but interesting backstory. Maybe points 1 and 3 could be killed with one stone.
Anyway this is sort of my basic premise on what I would like to see, I know others eschew the military aspect of ST and prefer other aspects and I would not want it to be wholly military, indeed a lot of my favorite episodes have no military conflict. But I would like to use that as the setting premise, would be great to juxtaposition the peace with the oncoming conflict.