I recall the prop stopping on the Bulldog (Lycoming again) a few times whilst spinning. It was something we used to brief solo students to be aware of before they went off doing solo aeros.
It was almost as if the initial entry to the spin provided enough rolling motion for the aircraft to "catch up with the prop" slightly and it would fail to go over compression, especially if the idle speed was a little too low. Effectively you have "stalled" the engine, very similar to stalling a car engine when not using enough throttle when pulling away.
Two ways to start it. One, obviously on the starter motor. Two, the recovery from the spin usually gave enough ergs back into the prop to rotate the engine and it would simply fire up and run again. The important thing was not to get disracted from the recovery or the spin could easily go high rotational, quite alarming in a 'Dog. It is worth noting that it's not generally the increased airspeed in the dive that gets the prop over compression, but the change in airflow through it caused by the pitching moment when recovering from the dive. So, if "fishtailing" doesn't work, try pulling a little 'G'.