I come back to what I said earlier - when they make these planes in the factory, they all start! If they didn't they wouldn't send them out.
Not sure about that. I flew a nearly-new SR22 a couple of years ago that had some kind of fancified hot-rodded engine (I think they called the plane a "Millenium Edition"). It was incredibly hard to start, which the instructors all knew about. You had to prime it exactly the right amount, and have the mixture and throttle in exactly the right position, and even once it had started, you had to nurse it for 30 seconds, gradually advancing the throttle and mixture at JUST the right speed, or it would cough and die - and refuse to start again. What a pain.
When I started flying I had a share in a (then) new 182, with injection. It was amazingly hard to start after a short shutdown, although I never actually failed. Everyone assumed the problem was vapour locks. You would try every trick in the book - mixture lean, mixture full rich, throttle open, throttle closed, no prime, lots of prime - and eventually one of them would catch its attention and it would start. Stone cold, it started first time every time.
My TR182, which is a carb engine, starts like a dream, whether hot or cold.
n5296s