I was aboard USS Omaha - we had a few 'experimental' systems aboard. The LA class subs had a lot of new ideas incorporated into them that made them (at the time) MUCH quieter than their opponents. I've heard of some of the ideas on later classes, and most had their origin in the LA class.

Since letting this lay fallow there have been two main ideas I've had about how to make this system work. 

1) Action Points and Phases
Instead of having set phases of movement, combat, etc.  each phase will be one boat performing all of it's actions.  The two exceptions to this (as of now) would be defensive fire against enemy torpedoes during that enemy's phase and damage control attempts at the end of the round.  Also as a way of limiting what a crew can do each boat is assigned a number of Action Points.  They use these to attempt to move to a different area (see below about areas), fire a weapon offensively, use sensors to develop a firing solution against one target or perform other actions during their phase.  So the advantage of going first would be the ability to damage or destroy an enemy boat and/or its systems before it can respond.  The disadvantage would be having to make the call on how man APs to reserve for defensive fire/damage control and the chance of not having enough APs or in losing APs held in reserve, but not used at the end of the turn.

2) Cat in the box
The one thing that's really been giving me a headache is how to maintain the uncertainty  of where the enemy is without resorting to a double blind game or having the system be so complex that it spawns its own headaches.  The idea that I've come up with are what I'm calling "Heisenberg Areas".  In short the enemy can be made uncertain about your exact location if you're not sure yourself.  What I'm doing is ditching my beloved hexes for an area movement system.  The knowledge you (and your enemy) not have is what general area you are in and what other areas you have the potential to move into.  They way I'd see this working for movement is you spend an Action Point and then you roll a d10 add your Drive system rating and if you have a 10 or more you move into the new area.  If not then you can spend another AP and try again, adding your accumulated total, or abandon the move if you're out of APs. 

That's where I'm at right now.  Just trying to distill my thoughts into something that can be used to run a scenario and see how it all hangs together.