Maybe I'm misunderstanding your "other way", but it sounds to me like the way I drive all the time and not double clutching at all. You are right in your first method of double clutching and that it is for older cars (which don't have synchros).
If you use the first method you listed, go ahead and do all that. It's still a waste of time in my mind. In a race, I'd prefer the engine to be engaged with the wheels rather than pushing the clutch in and out several times among other things I listed above.
Star Stage III