This may be totally unrelated, but I had an issue with the distributor on a Duetto 1600. It started reliably but it was missing intermittently and then started to get worse. In an effort to verify and adjust the ignition timing and point gap, I was getting erratic results when trying to turn the engine till the points just opened. Sometimes a 5-7 degree difference in the timing mark when the points opened. To make a long story short, the drive dog on the distributor shaft had worn the hole for the roll pin into an oblong shape allowing the timing to vary widely. You can see it on the attached picture. I wonder if something like this could allow enough variation in the timing to cause a no start situation and then when you roll the car it somehow changes the relation of the roll pin in the drive dog to get the timing closer to correct? I am not sure how pushing the car "in nuetral" could possibly transfer any motion to the engine to change anything, it seems unlikely but... just a thought.