I don't think there is an easy solution in terms of auto-targeting as there are too many factors that can be involved.
As for re-targeting I do think it should come at a cost in terms of time for missiles to re-target if their primary target is killed. I have no problems otherwise if missile re-target if the primary objective is gone.
I'm less concerned about efficiency or some very obscure scenario involving a thousand ships in a single battle. I like mechanics to make sense first and worry about busywork second. Even if making things easy on the player is important it is still secondary in my opinion.
I think that requiring time to re-target is an excellent compromise. It encourages spreading out fire to a degree, but still allows for re-targeting to be possible.
I agree that mechanics should make sense, but I do think that busywork is important to control as well. Certainly too much automation is not fun, but robust automatic systems allow the player to focus on what they WANT to focus on. But from a realism perspective, each of those ships has a captain and many crewmembers who would realistically be able to handle some targeting priorities. That is something that should be considered.
Perhaps a reaction roll, or crew training could be involved with retargeting as well? There are, after all, instant links to these missiles via TN, so a good tac officer should be 'playing' the missiles all the way to the target. In fact, I think crew/officer skills should be more involved in missiles in general, changing how effective ECM/ECCM is for example. A good crew with excellent officers should be able to significantly increase combat power in a way that isn't currently modeled with missiles, apart from fire rate.
In theory, if the fire control is in range, it ought to be possible to retarget missiles from incoming salvos to new targets...which...might already be possible in c#? I dunno, I've honestly not had it come up in most of my combats. But certainly missiles are by default controlled from the ship, since if the fire control goes down, they self-destruct lacking sensors. So in theory, shouldn't that control work in our favor as well?