I've missed second a couple times too...maybe even more than third ( i dont miss third very much if ever) but i have second. I've developed a bad habit when casual driving to lazily have my hand on the shifter...not good for powershifting.
A different shifter won't save you. Maybe you're getting stage fright. Calm down, and run it like you own the track, and everyone is in their underwear. Just don't look at them while you're going down the track.
Ed: Keep in mind, it is true that time spent shifting is time not accelerating, BUT, your goal isn't a certain SPEED, it's a certain DISTANCE, so even though you're not accelerating, you are still moving towards your goal at ~40, ~60, and ~90mph, so shifting .10 second faster isn't going to shave .10 second off your time. So, shift hastily, not rapid quick. Firm, but not wild. Some people break stuff, or just mess up when they get wild.
If you were trying to get to a certain speed, like 0-100mph, then yeah, shifting .10 faster will shave prolly .101 off your time. Extra .001 for the speed loss during a shift.