Based on what you've told me and what I'm actually experiencing, I have a theory:
The ignitor "wobbles" on the plug (both when I attach it and when I tried to charge it on the wall wart (light on plug flickers at times). When I start rotating the prop, the plug is not hot enough (due to poor contact) and the fuel keeps flowing as the cranking continues. When the plug eventually gets hot (because I adjust the igniter) and starts to fire, the engine is already flooded and can't continue when the igniter is removed.
The igniter needs to be able maintain constant contact with the plug so it fires before the engine floods.
Sound plausible?