My son Tyler is now shooting 3-gun for the Army Marksmanship Unit. He and I both started 3-gun competitions with little to no competition shooting experience. He was recruited because of the natural talent he showed at the major matches we went to.
The interesting thing I learned from him was the fact that they don't practice until they are knee deep in brass. They shoot relatively very few rounds, but the rounds they do shoot, they have timed with a timer and keep track of those times. Speaking from a 3-gun perspective, this is what he told me to work on.
1. Getting into or out of shooting positions as fast as possible - log the time from the movement until the shot.
2. Weapons transitions - the time it takes to safely ground one weapon and pick up another one and fire the shot.
3. Time to first shot - with handgun, shotgun, and rifle, from all different positions and weapons locations.
4. Target transitions
5. Reloads with all three weapons. Find what works the best for you based on the timer.
6. Shooting on the move and reloading on the move.
7. When you move - MOVE FAST! (that was the biggest thing for me).
More match time is saved with these helpful hints, than you will ever save by reducing your shot split times by .01 seconds. Basically, he told me to work on the "little" things, because he felt I already had a handle on the more major shooting challenges.
I find the shooting sports to not be a lot different than the OPs original analogy. In MMA if you don't have the moves, strikes, blocks, kicks, and holds already commited to your subconcious, you will never be able to "conciously" put these things into use fast enough to defend yourself. In shooting, if you don't have the above items commited to subconcious competence (you really don't need to think about it), you will be slower on your courses of fire than someone who does these things without even having to think about them.
Prior to Tyler going to the AMU we had received no type of competition type training. Everything was picked up from some extremely good and helpful local shooters like Keith, Bob Mills, Mark Peters, Tom Dalton, Pitel, etc..
For a good start to your training, get in touch with Mike Seeklander from USSA in Tulsa OK. He is their lead instructor and he will hook you up with a personal training regiment that can be constantly upgraded as you improve. This is mostly done on line, but it is a good way to learn from one of the best without the expense of going to classes. Take what you have learned to some local matches and use those matches as your personal training ground, don't worry about your placings. Seek advice from some of the people that are obviously very good at what they do and they are generally very open to offering advice, this is kind of a unique situation with the shooting sports. Note: just wait to speak with these people until after they have shot their course of fire so that they are allowed to concentrate on their own match without undue distraction.
Final note: If you go to
http://www.brianenos.com there is a lot of very usable information there. If you go the "Range Diary" section, look for a post titled "Cha-Lee's Tale". This shooter has kept a range diary from when he first started shooting a couple of years ago, and how he has progressed to the Grand Master level in Limited division of the USPSA. The diary is complete with how has practiced, to how he broke down stages at matches, then a brief video of him shooting that stage. It is almost like taking a class from this gentleman. Very good information that I have found very educational.
Good luck in your journey.
PS - come to a local 3-gun shoot if you get a chance!