I'm not police or military, and I've never been in a gunfight. My only experience that relates to your question is having competed in boxing and submission grappling.
Every fight I've ever had (in the ring/on the mats-- not on the street) I've been as prepared for as anybody could be, both in terms of conditioning and in terms of how many hundreds or thousands of rounds I've done training full contact with very good fighters. What I've found: unfortunately nothing has ever prepared me for the adrenaline and the twisted-up stomach I feel when I'm standing in my corner in front of a crowd, waiting for the action to start, wondering if this will be the time that I get seriously injured, humiliated, etc.
But as soon as the bell rings and the fight starts, a funny thing happens: it's like my mind gets shut off and suddenly what I'm doing is really no different from what I've done so many times before. I stop hearing the crowd, and think of only the moment I'm in, and everything becomes automatic.
However, I also always run out of gas a lot faster in a fight than I do in even the hardest sparring, which means I'm not as relaxed as I should be. Higher levels of muscular tension suck the oxygen right out of my blood. I have never once felt that I've performed up to my potential in a fight-- it's like I regress a year or two every time, losing maybe 30% of the skill level I walked in with. It's frustrating. I know of no way around it.
As they say, you don't rise to the occasion, you fall to the level of your training. (Something like that, anyway.) In my experience, you don't even get to function at the level of your training-- you fall to, at least in my case, 70% or so of your training.
One interesting thing I've seen recommended and tried myself a few times: next time you're at a range that will allow it, try dropping and doing 20 push-ups and immediately pop up and start firing. I've also tried running uphill sprints in National Forest out in the Sierras and then shooting. It's amazing how much your own heartbeat will move the handgun/ rifle/ shotgun around, and how close you come to that feeling of tunnel vision when you're sucking wind. Give it a shot.
Everybody else on here w/ real combat experience and training has much better advice for you, but that's the best I can offer. Since you're going to revert to a level even lower than whatever your training is, you'd better train hard and train often!