I carry my drivers license and permit in a credit card sized leather ID holder.
I was pulled over recently and had plenty of time to turn off the engine, and get my ID holder out before the LEO got to the door.
I didn't attempt to get the registration out until after I gave him my license and permit and let him know I was armed.
I used to be worried about getting this stuff out before the LEO approached but don't worry about it anymore.
I see no problem with pulling over, turning off the engine (depending on the weather), turning on the dome light, letting the LEO know I have a permit and am armed and simply following the his directions.
Like Sixto said in a previous thread, we are over thinking this problem.