I've mentioned it elsewhere, but it's an idea I tried to throw around just after VOY died.
Set just after the end of VOY, another Intrepid-class long-range exploration vessel, the USS Meriwether Lewis, explores the Gamma Quadrant. Hearkens back to the glory days of TOS - no immediate backup, Starfleet's up to a week away even by hyperchannel, the captain is on his/her own a lot (although still has to justify everything to Command later, so not too far off the reservation...). Every so often, they'll need to make a trip back to DS9 for resupply, although probably also setting up supply caches as they explore the quadrant (so they don't have to stay within a few days of the wormhole at all times).
What is the political situation in the quadrant like, now that the Founders have withdrawn to the Great Link for a time? Are there rogue Jem'Hadar who refuse to accept the surrender? Vorta who have become disillusioned with their gods, and if so, what form does their apostasy take? What foes kept the Jem'Hadar sharp, and the Founders on their guard, before the Wormhole brought them into contact with the Federation?
(Remember, the novels are non-canon - as far as canonical sources, the quadrant's completely open. Minimal continuity snarls possible, unlike Alpha Quadrant.)
I've been thinking along a similar vein for some time. Its nice to know I wasn't totally bonkers (I like the ship's name, btw! It invokes the feeling of rugged frontier exploration)
In my version, which never selected a quadrant, there is not one ship, but a small fleet, primarily 3 ships: a heavily armored command ship under a fleet captain, and two lighter ships, possibly an Intrepid-class as one of them. Their job is to 1) explore, 2) select prime locations for the establishment of "forts" (small bases for trade, repair, and resupply), 3) and guard colony ships and terraforming teams which hope to establish on any habitable worlds found. So rather than running in a straight line, it will be as the flow of explorers, traders, and settlers did on the American west: explore, fort, settlers, rinse, repeat. Each "fort" allows the fleet to probe deeper than before, while allowing a small measure of repair and resupply (though not at the level of a full starbase). There's enough mission variety in that mix to tell a lot of stories.