Alrighty, this post has to do with ship interiors and I want to take a page from a game many of you guys most likely played: Mass Effect.
Now I know ship sizes would make this model a bit different, but understand we don't need to see EVERY part of the ship. Just make those famous circular corridors on whatever deck we need to travel to and you have honestly made things perfectly fine. One place to go + giant circular corridor = Star Trek.
Anwyays, more specifically to the point what I think would be far more immersive and make ships seem more like ships than avatars would be focus of being INSIDE the ship when not in combat situations. You could even pull it back to have it be so when not on a mission or flying at impulse. Ship interiors need to be part of the game and the Mass Effect model can do so without problems.
First, ship interiors should replace the current sector space. I would much rather be staring at repeating warp animation than this map. Sounds strange, but its true. If I want to plot my course I can do it in an actual astrometrics (even if it is in a room directly connected to the bridge). This would not only allow characters to roam the ship, perhaps go to sickbay's and engineering, etc. For enemy encounters and other ship notifications obviously it would be as simple as having the captain be called to the bridge or accepting the commands to enter system right then and there. For Enemy signal contacts specifically, a yellow alert on the ship could be triggered, telling you to get to the bridge ASAP and prepare for combat or possibly avoid them.
This would make course plotting a bit more of a skill, knowing how to plot a course that avoids signal contacts but gets you to your destination faster. This would also help avoid instanced sectors, because systems would be a certain amount of "time" away, not distance. For everything else, though, a simple animation of the ship warping in from the bridge's perspective and a pan to the outside of the ship would put you right back in the usual interface.
PS: I would also like to see actual schematics of my own ship on the bridge, as well as a real-time view of whatever is in front of my ship when I'm on the bridge. If I'm in sector space, put a warp animation. At a planet, give me an image of the system I'm actually in. Staring at a brown nebula while orbiting Earth is a bit strange.